Square root of 5008

The square root of 5008 is 70.767224 (rounded to 6 decimal places). In simplest radical form it is 4√313.

Square root of 5008

Pick any whole number from 1 to 10,000.

\sqrt{5008} = 4\sqrt{313} \approx 70.767224

How to work it out

1
The square root of 5008 is the number that multiplied by itself gives 5008.
2
5008 is between the perfect squares 70² = 4900 and 71² = 5041, so its square root is between 70 and 71.
3
Pull out the biggest square factor: 5008 = 16 × 313, so
$\sqrt{5008} = \sqrt{16 \times 313} = 4\sqrt{313}$
4
A calculator, or long division of digits, gives
$\sqrt{5008} \approx 70.767224$

LaTeX source of the formulas on this page

\[ \sqrt{5008} = 4\sqrt{313} \approx 70.767224 \]
\[ \sqrt{5008} = \sqrt{16 \times 313} = 4\sqrt{313} \]
\[ \sqrt{5008} \approx 70.767224 \]

What is the square root of 5008?

The square root of 5008 is 70.767224 (rounded to 6 decimal places). In simplest radical form it is 4√313.

Is 5008 a perfect square?

No. It lies between 70² = 4900 and 71² = 5041.

What is 5008 squared?

5008 × 5008 = 25080064.

What is the square root of 5008 rounded to 2 decimals?

70.77.