The square root of 152 is expressed as √152 in the radical form and as (152)½ or (152)0.5 in the exponent form. The square root of 152 rounded up to 7 decimal places is 12.3288280. It is the positive solution of the equation x2 = 152. We can express the square root of 152 in its lowest radical form as 2 √38.

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Square Root of 152: 12.328828005937952Square Root of 152 in exponential form: (152)½ or (152)0.5Square Root of 152 in radical form: √152 or 2 √38

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1.What is the Square Root of 152?
2.How to find the Square Root of 152?
3.Is the Square Root of 152 Irrational?
4.FAQs

The square root of 152, (or root 152), is the number which when multiplied by itself gives the product as 152. Therefore, the square root of 152 = √152 = 2 √38 = 12.328828005937952.

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Value of √152 by Long Division Method

Explanation:

Forming pairs: 01 and 52Find a number Y (1) such that whose square is Bring down the next pair 52, to the right of the remainder 0. The new dividend is now 52.Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 2) such that 2Z × Z Divide 52 by 22 with the quotient as 2, giving the remainder = 52 - 22 × 2 = 52 - 44 = 8.Now, let"s find the decimal places after the quotient 12.Bring down 00 to the right of this remainder 8. The new dividend is now 800.Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 3) such that 24Z × Z Divide 800 by 243 with the quotient as 3, giving the remainder = 800 - 243 × 3 = 800 - 729 = 71.Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 152.

Therefore, the square root of 152 by long division method is 12.3 approximately.


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Example 1: Solve the equation x2 − 152 = 0

Solution:

x2 - 152 = 0 i.e. x2 = 152x = ±√152Since the value of the square root of 152 is 12.329,⇒ x = +√152 or -√152 = 12.329 or -12.329.


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FAQs on the Square Root of 152

What is the Value of the Square Root of 152?

The square root of 152 is 12.32882.

Why is the Square Root of 152 an Irrational Number?

Upon prime factorizing 152 i.e. 23 × 191, 2 is in odd power. Therefore, the square root of 152 is irrational.

What is the Value of 10 square root 152?

The square root of 152 is 12.329. Therefore, 10 √152 = 10 × 12.329 = 123.288.

What is the Square Root of -152?

The square root of -152 is an imaginary number. It can be written as √-152 = √-1 × √152 = i √152 = 12.328iwhere i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 152?

The square of the square root of 152 is the number 152 itself i.e. (√152)2 = (152)2/2 = 152.

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If the Square Root of 152 is 12.329. Find the Value of the Square Root of 1.52.

Let us represent √1.52 in p/q form i.e. √(152/100) = 1.52/10 = 1.233. Hence, the value of √1.52 = 1.233