The square root of 72 in simplified radical form is 6√2. Root 72 is denoted by √72 and its simplest form is given by 6√2. The value of root 72 is equal to 8.485.
Highlights of Root 72:
- Simplified radical form of root 72 is 6√2.
- 72 is not a perfect square number.
- Root 72 is NOT a rational number.
- Value of root 72 = 8.485 corrected up to 3 decimal places.
Table of Contents
What is Root 72 in Simplified Radical Form?
Answer: 6√2 is the simplified radical for of square root of 72.
Explanation:
At first, we will find out the perfect numbers (square of a number) that divide 72. Observe that 4 and 9 are perfect numbers that divide of 72. We have:
72 = 4 × 9 × 2.
Taking square on both sides, we have that
$\sqrt{72} =$ $\sqrt{4 \times 9 \times 2}$
⇒ √72 = √4 × √9 × √2, using the rule of indices ${\color{orange}\sqrt{abc}=\sqrt{a} \times \sqrt{b} \times \sqrt{c}}$
⇒ √72 = 2 × 3 × √2
⇒ √72 = 6√2.
Square Root of 72 by Prime Factorization Method
To find the square root of 72 by the prime factorization method, let us first write down the prime factorization of 72 which is given as follows:
72 = 2 × 2 × 2 × 3 × 3.
Therefore, √72 = √(2 × 2 × 2 × 3 × 3)
⇒ √72 = 2 × 3 × √2
⇒ √72 = 6√2.
So the simplest form of square root of 72 by prime factorization method is equal to 6√2.
Also Read: Square root of 108 in simplified radical form
Value of Square Root of 72
As √72 = 6√2 and √2 = 1.414, so the value of square root of 72 is equal to
√72 = 6√2 = 6 × 1.414 = 8.485.
Hence, the value of root 72 is equal to 8.485 corrected up to three decimal places.
More Topics: Square root of 50
Is Square Root of 72 Rational?
Answer: As √72 = 6√2 and √2 is an irrational number, we conclude that square root of 72 is not a rational number.
More Reading:
Is 72 a Perfect Square?
Answer: As √72 = 6√2, so square root of 72 is not a whole number. This proves that 72 is not a perfect square number.
FAQs
Answer: 6√2 is the simplest form of square root of 72.
Answer: The simplified radical form of root 72 is equal to 6√2. So root 72 is a quadratic surd.
Answer: Thee value of root 72 is 6√2. As √2 is irrational, this makes square root of 72 an irrational number.
Answer: As the square root of 72 is 6√2, not an integer, the number 72 is not a perfect square.
This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.