Square Root of 1400
The square root of 1400 is expressed as √1400 in the radical form and as (1400)^{½} or (1400)^{0.5} in the exponent form. The square root of 1400 rounded up to 9 decimal places is 37.416573868. It is the positive solution of the equation x^{2} = 1400. We can express the square root of 1400 in its lowest radical form as 10 √14.
 Square Root of 1400: 37.416573867739416
 Square Root of 1400 in exponential form: (1400)^{½} or (1400)^{0.5}
 Square Root of 1400 in radical form: √1400 or 10 √14
1.  What is the Square Root of 1400? 
2.  How to find the Square Root of 1400? 
3.  Is the Square Root of 1400 Irrational? 
4.  FAQs 
What is the Square Root of 1400?
The square root of 1400, (or root 1400), is the number which when multiplied by itself gives the product as 1400. Therefore, the square root of 1400 = √1400 = 10 √14 = 37.416573867739416.
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How to Find Square Root of 1400?
Value of √1400 by Long Division Method
Explanation:
 Forming pairs: 14 and 00
 Find a number Y (3) such that whose square is <= 14. Now divide 14 by 3 with quotient as 3.
 Bring down the next pair 00, to the right of the remainder 5. The new dividend is now 500.
 Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 7) such that 6Z × Z <= 500. After finding Z, together 6 and Z (7) form a new divisor 67 for the new dividend 500.
 Divide 500 by 67 with the quotient as 7, giving the remainder = 500  67 × 7 = 500  469 = 31.
 Now, let's find the decimal places after the quotient 37.
 Bring down 00 to the right of this remainder 31. The new dividend is now 3100.
 Add the last digit of quotient to divisor i.e. 7 + 67 = 74. To the right of 74, find a digit Z (which is 4) such that 74Z × Z <= 3100. Together they form a new divisor (744) for the new dividend (3100).
 Divide 3100 by 744 with the quotient as 4, giving the remainder = 3100  744 × 4 = 3100  2976 = 124.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1400.
Therefore, the square root of 1400 by long division method is 37.4 approx.
Is Square Root of 1400 Irrational?
The actual value of √1400 is undetermined. The value of √1400 up to 25 decimal places is 37.41657386773941385583749. Hence, the square root of 1400 is an irrational number.
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 Square Root of 49  √49 = 7
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Square Root of 1400 Solved Examples

Example 1: Solve the equation x^{2} − 1400 = 0
Solution:
x^{2}  1400 = 0 i.e. x^{2} = 1400
x = ±√1400
Since the value of the square root of 1400 is 37.417,
⇒ x = +√1400 or √1400 = 37.417 or 37.417. 
Example 2: If the area of a circle is 1400π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 1400π in^{2}
⇒ r = ±√1400 in
Since radius can't be negative,
⇒ r = √1400
The square root of 1400 is 37.417.
⇒ r = 37.417 in 
Example 3: If the surface area of a cube is 8400 in^{2}. Find the length of the side of the cube.
Solution:
Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a^{2} = 8400 in^{2}
⇒ a = ±√1400 in
Since length can't be negative,
⇒ a = √1400
We know that the square root of 1400 is 37.417.
⇒ a = 37.417 in
FAQs on the Square Root of 1400
What is the Value of the Square Root of 1400?
The square root of 1400 is 37.41657.
Why is the Square Root of 1400 an Irrational Number?
Upon prime factorizing 1400 i.e. 2^{3} × 5^{2} × 7^{1}, 2 is in odd power. Therefore, the square root of 1400 is irrational.
What is the Square Root of 1400 in Simplest Radical Form?
We need to express 1400 as the product of its prime factors i.e. 1400 = 2 × 2 × 2 × 5 × 5 × 7. Therefore, √1400 = √2 × 2 × 2 × 5 × 5 × 7 = 10 √14. Thus, the square root of 1400 in the lowest radical form is 10 √14.
Evaluate 10 plus 9 square root 1400
The given expression is 10 + 9 √1400. We know that the square root of 1400 is 37.417. Therefore, 10 + 9 √1400 = 10 + 9 × 37.417 = 10 + 336.749 = 346.749
What is the Square of the Square Root of 1400?
The square of the square root of 1400 is the number 1400 itself i.e. (√1400)^{2} = (1400)^{2/2} = 1400.
If the Square Root of 1400 is 37.417. Find the Value of the Square Root of 14.
Let us represent √14 in p/q form i.e. √(1400/100) = 14/10 = 3.742. Hence, the value of √14.0 = 3.742