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Square Root of 175

Did you know that 175 can be expressed as the sum of its digits raised to successive integer powers as 175 = 1¹+ 7² + 5³? The other numbers following this property are 135, 518, 598, and 1306. In this lesson, we will learn to calculate the square root of 175 by long division method. We will also go through a few solved examples and interactive questions related to the square root of 175.

Square Root of 175: √175 = 13.228
Square of 175: 175² = 30,625

1.	What Is the Square Root of 175?
2.	Is Square Root of 175 Rational or Irrational?
3.	How to Find the Square Root of 175?
4.	FAQs on Square Root of 175

What Is the Square Root of 175?

The square root of 175 is defined as the value obtained on the multiplication of an integer by itself which will give the final product as 175. As there is no such integer which on multiplication with itself will give 175 exactly, the square root of 175 is not a whole number.

Is the Square Root of 175 Rational or Irrational?

The square root of 175 can be approximately written as 13.228. This is a non-recurring and non-terminating decimal number. This shows that 175 is not a perfect square which also proves that the square root of 175 is an irrational number.

Tips and Tricks:

175 is not a perfect square. Its square root is an irrational number. The square root of any number n, which is not a perfect square, will always be an irrational number.

How to Find the Square Root of 175?

The square root of 175 can be found using the following steps:

Step 1: First we will check whether the number is a perfect square or not. 175 is not a perfect square as it cannot be broken down into a product of two same numbers.
Step 2: Once the number is checked, we can do the following:

A number which is a perfect square can be written as √x² = x.
For a number which is not a perfect square, the square root can be found using the long division method. This number can be written in its simplified radical form of the square root.

In this case, 175 is not a perfect square. Hence, its square root is found using the long division method. The simplified radical form of the square root of 175 is given below.

Simplified Radical Form of Square Root of 175

175 can be written as the product of 25 and 7. It is given as:

√175 = √(25 × 7)

7 is not a perfect square. Hence, it stays within the root sign. 25 can be shown as 5². Thus, the simplified radical form of the square root of 175 is 5√7.

Square Root of 175 by Long Division Method

The square root of 175 can be found using the long division method. These are the steps to be followed:

Step 1: We will start pairing the digits from the right. We will pair up the digits by putting a bar above them.
Step 2: We will find a number such that when it is multiplied with itself, the product is less than or equal to 175. Keeping the divisor as 23, we get the quotient as 13 and the remainder 75-69 = 6.
Step 3: Double the divisor and enter it with a blank on its right. Then assume the digit to replace the blank such that when the new divisor is multiplied to the new quotient, the final product will be lesser than or equal to our dividend. Finally, divide and write the remainder. Let's repeat the above step. Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal places you want.

Hence, √175 = 13.228

Explore square roots using illustrations and interactive examples

Challenging Questions:

How will Hailey find the square root of 175 using the long division method up to 7 decimal places?
How will Mandy express the square root of 525 in terms of the square root of 175?

Example 1: Help Julie find two consecutive numbers between which the value of the square root of 175 lies.

Solution

The perfect squares closer to 175 are 169 and 196. The square root of 169 is 13. The square root of 196 is 14. Hence, the two numbers between which the square root of 175 lies are 13 and 14.
Example 2: What is the diameter of a circle if its area is 175π square inches?

Solution

The area of circle is given as πr².
Hence, area = πr² = 175π ⇒ r² = 175 ⇒ r = √175 = 13.228 ≈ 13.2 inches.
As, d = 2r = 2 × 13.2 = 26.4 inches. Hence, the diameter of a circle if its area is 175π square inches is 26.4 inches.

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FAQs on Square Root of 175

What is the square root of 175 in the simplest form?

The square root of 175 in the simplest form is 5√7.

How do you find the square root of 175?

175 is not a perfect square number. Hence, the square root of 175 is obtained using the long division method.

What is the approximate square root of 175?

The square root of 175 is 13.2287 (approximately).

Is the square root of 175 rational or irrational?

The square root of 175 is irrational.

Is the square root of 175 a real number?

Yes, the square root of 175 is a real number.

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