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.
