Square root of 7648

The square root of 7648 is 87.452844 (rounded to 6 decimal places). In simplest radical form it is 4√478.

Square root of 7648

Pick any whole number from 1 to 10,000.

\sqrt{7648} = 4\sqrt{478} \approx 87.452844

How to work it out

1
The square root of 7648 is the number that multiplied by itself gives 7648.
2
7648 is between the perfect squares 87² = 7569 and 88² = 7744, so its square root is between 87 and 88.
3
Pull out the biggest square factor: 7648 = 16 × 478, so
$\sqrt{7648} = \sqrt{16 \times 478} = 4\sqrt{478}$
4
A calculator, or long division of digits, gives
$\sqrt{7648} \approx 87.452844$

LaTeX source of the formulas on this page

\[ \sqrt{7648} = 4\sqrt{478} \approx 87.452844 \]
\[ \sqrt{7648} = \sqrt{16 \times 478} = 4\sqrt{478} \]
\[ \sqrt{7648} \approx 87.452844 \]

What is the square root of 7648?

The square root of 7648 is 87.452844 (rounded to 6 decimal places). In simplest radical form it is 4√478.

Is 7648 a perfect square?

No. It lies between 87² = 7569 and 88² = 7744.

What is 7648 squared?

7648 × 7648 = 58491904.

What is the square root of 7648 rounded to 2 decimals?

87.45.