Square Root of 72 - How to Find the Square Root of 72? - Cuemath?

Hence, √72 lies between √64 and √81, i.e., √72 lies between 8 and 9. Square root of a non-perfect square number in the simplest radical form can be found using prime factorization method. For example: 72 = 2 × 2 × 2 × 3 × 3. So, √72 = √(2 × 2 × 2 × 3 × 3) = 6√2 .

Which number is closest to √72?

Evaluating this, we find that the square root of 72 is approximately equal to 8.49. Consequently, √72 falls within the interval between 8 and 9 on the number line.

What is the perfect square of 72?

We can see that 72 is not a perfect square because a perfect square will have an even number of factors. We can also find the square root of 72 in an alternate method. Let us write 72 as a product of two numbers where each or one of these numbers are perfect squares. We can write 72 as a product of 2 and 36.

What is the square root function in Cuemath?

The square root function involves the square root symbol √ (which is read as "square root of") . The square root of a number 'x' is a number 'y' such that y 2 = x. i.e., if y 2 = x ⇒ y = √x. i.e., if 'x' is the square of 'y' then 'y' is the square root of 'x'.

What is the value of √72?

Square root of 72 is equal to 6√2 = 8.48528137424 …, i.e. √72 = 8.48528137424…

What are the factors of root 72?

Thus the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72 . Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

Where does the square root of 72 lie?

The number 72 lies between the perfect squares 64 and 81 . So, the square root of 72 lies between the square roots of these two numbers, which are 8 and 9 respectively. Since the square root of 72 is approximately 8.485, it falls between 8 and 9. The square root of 72 is not a whole number, as it is approximately 8.485.

What is the cube root of 72 simplified?

The cube root of 72 is the number which when multiplied by itself three times gives the product as 72. Since 72 can be expressed as 2 × 2 × 2 × 3 × 3. Therefore, the cube root of 72 = ∛(2 × 2 × 2 × 3 × 3) = 4.1602 .

What number squared gives you 72?

The closest square of a number to 72 is 8x8=64 +8 is 72. Therefore the number is 8.

What is the factorization of 72?

72 has a total of 12 factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. There is a trick to calculate the total number of factors of a number. For example, 72 = 2 × 2 × 2 × 3 × 3 = 2 3 × 3 2 . We get the prime factorizations of 72 as 2 3 × 3 2 .

How many digits are there in the square of 72?

Answer. Because the number has 2 digits, therefore it's square will have 4 digits .

How to calculate square root without a calculator?

Long division method Separate your square root base into pairs. ... Find the largest square that divides into the first number or pair. ... Subtract the square from the first number or pair. ... Drop down the next pair. ... Multiply the first digit of the square by two. ... Set up the next factor equation. More items... Aug 8, 2022

What are the factors of 72?

In other words, the factors of 72 are the numbers that are multiplied in pairs resulting in an original number 72. As the number 72 is a composite number, it has many factors other than one and the number itself. Thus the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72 .

How to simplify 4 square root of 72?

Expert-Verified Answer Simplification of the given expression 4 square root of 72 is equal to 24√2 or 33.94 . Therefore, simplification of the given expression 4 square root of 72 is equal to 24√2 or 33.94.

Square Root of 72 - How to Find the Square Root of 72?

72 is not a perfect square. Itis represented as√72. The square root of 72 can only be simplified.In this mini-lesson we will learn to find square root of 72by long division method along with solved examples. Let us see what the square root of 72is.

Square Root of 72:√72= 8.4852
Square of 72: 72² = 5184

1.	What Is the Square Root of 72?
2.	IsSquare Root of 72 Rational or Irrational?
3.	How to Find the Square Root of 72?
4.	FAQs on Square Root of 72

What Is the Square Root of 72?

The original number whose square is 72 is thesquare rootof 72. Can you find what is that number? Itcan be seen thatthere are nointegers whose square gives 72.

√72= 8.4852

To check this answer, we can find (8.4852)²and we can see that we get a number 71.99861904. This number is very close to 72when its rounded to its nearest value.

Is the Square Root of 72Rational orIrrational?

Any number which iseither terminating or non-terminating and has a repeatingpattern in its decimal part is arational number. We saw that√72= 8.48528137423857. This decimal numberis non-terminating and the decimal part has no repeating pattern. So it is NOT a rational number. Hence,√72is an irrational number.

Important Notes:

72lies between 64and 81. Hence,√72 lies between √64 and√81, i.e., √72lies between 8and 9.
Square root of a non-perfect square number in the simplest radical form can be found using prime factorization method. For example: 72= 2 × 2 × 2 × 3 × 3. So, √72=√(2 × 2 × 2 × 3 × 3)= 6√2.

How to Find the Square Root of 72?

There are differentmethods to find the square root of any number. We canfind the square root of 72 using long division method.
Click hereto know more about it.

Simplified Radical Form of Square Root of 72

72is a compositenumber. Hencefactors of 72are1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72. When we find the square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them. The factorization of 72is 2 × 2 × 2 × 3 × 3which has 1pairof the same number. Thus, the simplest radical form of √72is 6√2.

Square Root of 72by Long Division Method

The square root of 72can be found using the long division as follows.

Step 1: In this step, we pair off digits of a given number starting with a digit at one's place. We put a horizontalbar to indicatepairing.
Step 2:Now we need to find a number which on squaring gives value less than or equal to 72. As we know, 8× 8= 64 < 72. The divisor obtained is 8and the quotient is 8.
Step 3:Now, we have to bring down 00 and multiply the quotient by 2 which gives us 16.
Step 4: 4is writtenatone's place of new divisor because when 164is multiplied by 4, 656 is obtained which is less than 800. The obtained answer now is 144and we bring down 00.
Step 5: The quotient is now 84and itis multiplied by 2. Thisgives 168, which then would become the starting digit of the new divisor.
Step 6: 7is writtenatone's place of new divisor because when 1688is multiplied by 8, 13504is obtained which is less than 14400. The obtained answer now is 896 and we bring down 00.
Step 7: The quotient is now 848 and itis multiplied by 2. Thisgives 1696, which then would become the starting digit of the new divisor.
Step 8: 5is writtenatone's place of new divisor because when 16965is multiplied by 8, 84825is obtained which is less than 89600. The obtained answer now is 4775and we bring down 00.

So far we have got √72= 8.485. On repeating this process further, we get,√72= 8.48528137423857

Explore square roots using illustrations and interactive examples.

Square Root of 61
Square Root of 63
Square Root of 65
Square Root of 68
Square Root of 85

Think Tank:

Are√-72and -√72same ?
Is √-72a real number?

FAQs on Square Root of 72

Can the square root of 72be simplified?

Yes, the square root of 72canbe simplified and can be expressed in radical form as 6√2.

What is the square root of 72rounded to its nearest tenth?

Rounding off the square root of 72to its nearest tenth means to have one digit after the decimal point.
√72= 8.485can be rounded to its nearest tenth as 8.5.

Does 72have a square root?

Square root of 72can be written as6√2 andit cannot be simplified further as it is not a perfect square.

What is the square root of 72simplified?

72is not a perfect square and hence its square root is not a whole number. √72= 8.48528137423857 (approx.)

Is the square root of 72rational or irrational?

The square root of 72is irrational.

Is square root of 72a real number?

Yes, the square root of 72is a real number.

Square Root of 72 - How to Find the Square Root of 72? - Cuemath (2024)