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Square Root of 700

The square root of 700 is expressed as √700 in the radical form and as (700)^½ or (700)^0.5 in the exponent form. The square root of 700 rounded up to 8 decimal places is 26.45751311. It is the positive solution of the equation x² = 700. We can express the square root of 700 in its lowest radical form as 10 √7.

Square Root of 700: 26.457513110645905
Square Root of 700 in exponential form: (700)^½ or (700)^0.5
Square Root of 700 in radical form: √700 or 10 √7

Square Root of 700

1.	What is the Square Root of 700?
2.	How to find the Square Root of 700?
3.	Is the Square Root of 700 Irrational?
4.	FAQs

What is the Square Root of 700?

The square root of 700, (or root 700), is the number which when multiplied by itself gives the product as 700. Therefore, the square root of 700 = √700 = 10 √7 = 26.457513110645905.

☛ Check: Square Root Calculator

How to Find Square Root of 700?

Square Root of 700 by Long Division Method

Value of √700 by Long Division Method

Explanation:

Forming pairs: 07 and 00
Find a number Y (2) such that whose square is <= 7. Now divide 07 by 2 with quotient as 2.
Bring down the next pair 00, to the right of the remainder 3. The new dividend is now 300.
Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 6) such that 4Z × Z <= 300. After finding Z, together 4 and Z (6) form a new divisor 46 for the new dividend 300.
Divide 300 by 46 with the quotient as 6, giving the remainder = 300 - 46 × 6 = 300 - 276 = 24.
Now, let's find the decimal places after the quotient 26.
Bring down 00 to the right of this remainder 24. The new dividend is now 2400.
Add the last digit of quotient to divisor i.e. 6 + 46 = 52. To the right of 52, find a digit Z (which is 4) such that 52Z × Z <= 2400. Together they form a new divisor (524) for the new dividend (2400).
Divide 2400 by 524 with the quotient as 4, giving the remainder = 2400 - 524 × 4 = 2400 - 2096 = 304.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 700.

Therefore, the square root of 700 by long division method is 26.4 approx.

Is Square Root of 700 Irrational?

The actual value of √700 is undetermined. The value of √700 up to 25 decimal places is 26.45751311064590590501616. Hence, the square root of 700 is an irrational number.

☛ Also Check:

Square Root of 10 - √10 = 3.16228
Square Root of 34 - √34 = 5.83095
Square Root of 1000 - √1000 = 31.62278
Square Root of 116 - √116 = 10.77033
Square Root of 16 - √16 = 4
Square Root of 784 - √784 = 28
Square Root of 37 - √37 = 6.08276

Square Root of 700 Solved Examples

Example 1: Solve the equation x² − 700 = 0

Solution:

x² - 700 = 0 i.e. x² = 700
x = ±√700
Since the value of the square root of 700 is 26.458,
⇒ x = +√700 or -√700 = 26.458 or -26.458.
Example 2: If the area of an equilateral triangle is 700√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 = 700√3 in²
⇒ a = ±√2800 in
Since length can't be negative,
⇒ a = √2800 = 2 √700
We know that the square root of 700 is 26.458.
⇒ a = 52.915 in
Example 3: If the area of a square is 700 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 = 700 in²
⇒ a = ±√700 in
Since length can't be negative,
⇒ a = √700 = 26.458 in

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FAQs on the Square Root of 700

What is the Value of the Square Root of 700?

The square root of 700 is 26.45751.

Why is the Square Root of 700 an Irrational Number?

Upon prime factorizing 700 i.e. 2² × 5² × 7¹, 7 is in odd power. Therefore, the square root of 700 is irrational.

What is the Value of 15 square root 700?

The square root of 700 is 26.458. Therefore, 15 √700 = 15 × 26.458 = 396.863.

If the Square Root of 700 is 26.458. Find the Value of the Square Root of 7.

Let us represent √7 in p/q form i.e. √(700/100) = 7/10 = 2.646. Hence, the value of √7.0 = 2.646

Evaluate 3 plus 11 square root 700

The given expression is 3 + 11 √700. We know that the square root of 700 is 26.458. Therefore, 3 + 11 √700 = 3 + 11 × 26.458 = 3 + 291.033 = 294.033

What is the Square Root of -700?

The square root of -700 is an imaginary number. It can be written as √-700 = √-1 × √700 = i √700 = 26.457i
where i = √-1 and it is called the imaginary unit.

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