The square root of 153 in simplified radical form is equal to 3√17. Note that root 153 is written as √153, so the value of √153 = 3√17. Here we will learn how to find the square root of 153 in its simplest form.
The square root of 153 simplified is given as follows:
√153 = 3√17.
Table of Contents
Square root of 153 in Simplest Radical Form
Answer: 3√17 is the simplest radical form of square root 153.
Solution:
To find the square root of 153 in its simplest radical form, at first we will write 153 as a product of two numbers; at least one of them will be a perfect square (1, 4, 9, 16, 25, etc are a few examples of perfect squares).
Note that 9 is a perfect square and it divides 117. We can write 153 as follows:
153 = 9 × 17.
Taking square root on both sides, we get that
$\sqrt{153}=\sqrt{9 \times 17}$
⇒ $\sqrt{153}$ $=\sqrt{9} \times \sqrt{17}$ using the square root formula √(a×b) = √a × √b.
⇒ $\sqrt{153}$ = 3 × √17 as the square root of 9 is 3.
⇒ $\sqrt{153}$ = 3√17
Therefore, the square root of 153 in simplified radical form is 3√17.
Is 153 a perfect square number?
No, 153 is not a perfect square number. This is because, we know √153 = 3√17 and √17 is not an integer.
As √17 is an irrational number and √153 = 3√17, so square root of 153 is not a rational number.
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FAQs on Square Root of 153
Answer: Note that 153 = 3 × 3 × 17. So the square root of 153 is equal to √(3 × 3 × 17) = 3√17. So 3√17 is the radical form of square root of 153.
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.