# Square Root of 17

Proof that the square root of ANY integer is irrational (besides perfect squares)
Proof that the square root of ANY integer is irrational (besides perfect squares)

The square root of 17 is defined as a number that, when multiplied by itself twice, yields the original number 17. Because it cannot be expressed in the form p/q, the square root of 17 is an irrational number. In this article, we will go over two methods for finding the square root of 17, including the long division method and the estimation method, with detailed explanations for each.

## What is the Square Root of 17?

The square root of 17 is a number, which is the result of multiplying a number by itself and getting the result 17. √17 represents the square root of 17, symbolically.

As a result of this, √17 = √(Number×Number)

Hence, multiplying 4.123 twice, the original number 17 is obtained.

(.e.) √17 = √(4.123 × 4.123)

√17 = √(4.123)2

On removing the square and square root, we obtain

√17 = ±4.123

 Square Root of 17 in Decimal Form: 4.123

## Square Root of 17 by the Estimation Method

In the estimation method, find a whole number greater than the square root of 17, and a whole number less than the square root of 17.

It is important to note that the square roots of 18, 19, 20, 21, 22, 23, 24, and 25 are all greater than the square root of 17.

However, only √25 produces a whole number, so this is the one we will use.

Second, we’ll look for a number that is less than 17.

Because √16 gives a whole number, this is the one we’ll go with.

√16 = 4 because 4 × 4 = 16

So, we get 4 < √17 < 5

Hence, the square root of 17 is between 4 and 5. Thus, we could estimate the square of 17 to be 4.1.

## Square Root of 17 by the Long Division Method

Step 1: In the decimal form, write the number 17 as 17.000000. Now, pair the numbers from the right in pairs. We have 17 on the left. Find a number that, when multiplied by itself, equals 17 or less.

Step 2: So, we get 16 = 4 × 4. Subtract 16 from 17. Hence, the remainder is 1 and the quotient is 4. Now, bring one pair of zeros. So, the new dividend obtained is 100.

Step 3: Multiply the quotient by two and we get 8. Make the new divisor 80. Choose a number that, when added to 80 and multiplied by the result, is 100 or less.

Step 4: We find that adding 1 to 80 becomes 81, and 81×1 = 81. Subtract 81 from 100 and we have 19 as the remainder. Bring the next two zeros down. So, the new dividend is 1900.

Step 5: Multiply 41 by 2. We get the number 82. Make the new divisor 820. Choose a number that, when added to 820 and multiplied by the sum, equals or is less than 1900.

Step 6: We observe that 2 Plus 820 equals 822 and that 822×2 = 1644. Subtract 1644 from 1900 to obtain 256 as the remaining. Bring the next two zeros down. The new dividend is 25600.

Step 7: Continue the division operation until we get the approximate value of the square root of 17.

Step 8: As a result, the value of the square root of 17 is approximately equal to 4.123.

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## Video Lessons on Square Roots

### Examples

Example 1:

Simplify 2√17 + 14.

Solution:

Given: 2√17 + 14

As we know, the square root of 17 is 4.123.

Substituting the value in the expression,

2√17 + 14 = 2(4.123) + 14

2√17 + 14 = 8.246 + 14 = 22.246

Hence, the simplification of 2√17 + 14 is 22.246.

Example 2:

Determine the value of k, if k +√17=70.

Solution:

Given: k +√17=70. …(1)

We know that √17 = 4.123

Now, substitute the value in equation (1), we get

k + 4.123 = 70

k = 70 – 4.123

k = 65.877.

Therefore, the value of k is 65. 877.

Example 3:

Simplify the expression: 10√17 × 10√17

Solution:

Given expression: 10√17 × 10√17

10√17 × 10√17 = 100(√17)2

On removing square and square root, we get

10√17 × 10√17 = 100(17)

10√17 × 10√17 = 1700

Hence,10√17 × 10√17 is 1700.

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## Frequently Asked Questions on the Square Root of 17

### What is the value of the square root of 17?

The number √17 has a value of 4.123.

What is the radical representation of the square root of 17?

The square root of 17 is given in radical form as √17.

### Is the number seventeen a perfect square?

No, 17 is not a perfect square because it cannot be written as the product of two equal integers.

### Determine the square of the square root of 17.

The value of the square of the square root of 17 is 17.

(That is, √(17)2 = 17).

What is the sum of ten plus square root of 17?

We already know that √17 equals 4.123.
As a result, 10+4.123=14.123.

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