Square root of 5312

The square root of 5312 is 72.883469 (rounded to 6 decimal places). In simplest radical form it is 8√83.

Square root of 5312

Pick any whole number from 1 to 10,000.

\sqrt{5312} = 8\sqrt{83} \approx 72.883469

How to work it out

1
The square root of 5312 is the number that multiplied by itself gives 5312.
2
5312 is between the perfect squares 72² = 5184 and 73² = 5329, so its square root is between 72 and 73.
3
Pull out the biggest square factor: 5312 = 64 × 83, so
$\sqrt{5312} = \sqrt{64 \times 83} = 8\sqrt{83}$
4
A calculator, or long division of digits, gives
$\sqrt{5312} \approx 72.883469$

LaTeX source of the formulas on this page

\[ \sqrt{5312} = 8\sqrt{83} \approx 72.883469 \]
\[ \sqrt{5312} = \sqrt{64 \times 83} = 8\sqrt{83} \]
\[ \sqrt{5312} \approx 72.883469 \]

What is the square root of 5312?

The square root of 5312 is 72.883469 (rounded to 6 decimal places). In simplest radical form it is 8√83.

Is 5312 a perfect square?

No. It lies between 72² = 5184 and 73² = 5329.

What is 5312 squared?

5312 × 5312 = 28217344.

What is the square root of 5312 rounded to 2 decimals?

72.88.