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Square Root of 176

The square root of 176 is expressed as √176 in the radical form and as (176)^½ or (176)^0.5 in the exponent form. The square root of 176 rounded up to 6 decimal places is 13.266499. It is the positive solution of the equation x² = 176. We can express the square root of 176 in its lowest radical form as 4 √11.

Square Root of 176: 13.2664991614216
Square Root of 176 in exponential form: (176)^½ or (176)^0.5
Square Root of 176 in radical form: √176 or 4 √11

Square Root of 176

1.	What is the Square Root of 176?
2.	How to find the Square Root of 176?
3.	Is the Square Root of 176 Irrational?
4.	FAQs

What is the Square Root of 176?

The square root of 176, (or root 176), is the number which when multiplied by itself gives the product as 176. Therefore, the square root of 176 = √176 = 4 √11 = 13.2664991614216.

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How to Find Square Root of 176?

Square Root of 176 by Long Division Method

Value of √176 by Long Division Method

Explanation:

Forming pairs: 01 and 76
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 76, to the right of the remainder 0. The new dividend is now 76.
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 3) such that 2Z × Z <= 76. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 76.
Divide 76 by 23 with the quotient as 3, giving the remainder = 76 - 23 × 3 = 76 - 69 = 7.
Now, let's find the decimal places after the quotient 13.
Bring down 00 to the right of this remainder 7. The new dividend is now 700.
Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 2) such that 26Z × Z <= 700. Together they form a new divisor (262) for the new dividend (700).
Divide 700 by 262 with the quotient as 2, giving the remainder = 700 - 262 × 2 = 700 - 524 = 176.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 176.

Therefore, the square root of 176 by long division method is 13.2 approx.

Is Square Root of 176 Irrational?

The actual value of √176 is undetermined. The value of √176 up to 25 decimal places is 13.26649916142159939645973. Hence, the square root of 176 is an irrational number.

☛ Also Check:

Square Root of 1000 - √1000 = 31.62278
Square Root of 30 - √30 = 5.47723
Square Root of 19 - √19 = 4.35890
Square Root of 225 - √225 = 15
Square Root of 22 - √22 = 4.69042
Square Root of 256 - √256 = 16
Square Root of 324 - √324 = 18

Square Root of 176 Solved Examples

Example 1: Solve the equation x² − 176 = 0

Solution:

x² - 176 = 0 i.e. x² = 176
x = ±√176
Since the value of the square root of 176 is 13.266,
⇒ x = +√176 or -√176 = 13.266 or -13.266.
Example 2: If the area of an equilateral triangle is 176√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 176√3 in²
⇒ a = ±√704 in
Since length can't be negative,
⇒ a = √704 = 2 √176
We know that the square root of 176 is 13.266.
⇒ a = 26.533 in
Example 3: If the area of a square is 176 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 176 in²
⇒ a = ±√176 in
Since length can't be negative,
⇒ a = √176 = 13.266 in

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FAQs on the Square Root of 176

What is the Value of the Square Root of 176?

The square root of 176 is 13.26649.

Why is the Square Root of 176 an Irrational Number?

Upon prime factorizing 176 i.e. 2⁴ × 11¹, 11 is in odd power. Therefore, the square root of 176 is irrational.

What is the Square Root of -176?

The square root of -176 is an imaginary number. It can be written as √-176 = √-1 × √176 = i √176 = 13.266i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 176 is 13.266. Find the Value of the Square Root of 1.76.

Let us represent √1.76 in p/q form i.e. √(176/100) = 1.76/10 = 1.327. Hence, the value of √1.76 = 1.327

What is the Square Root of 176 in Simplest Radical Form?

We need to express 176 as the product of its prime factors i.e. 176 = 2 × 2 × 2 × 2 × 11. Therefore, √176 = √2 × 2 × 2 × 2 × 11 = 4 √11. Thus, the square root of 176 in the lowest radical form is 4 √11.

What is the Value of 8 square root 176?

The square root of 176 is 13.266. Therefore, 8 √176 = 8 × 13.266 = 106.132.

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