Square root of 7564

The square root of 7564 is 86.97126 (rounded to 6 decimal places). In simplest radical form it is 2√1891.

Square root of 7564

Pick any whole number from 1 to 10,000.

\sqrt{7564} = 2\sqrt{1891} \approx 86.97126

How to work it out

1
The square root of 7564 is the number that multiplied by itself gives 7564.
2
7564 is between the perfect squares 86² = 7396 and 87² = 7569, so its square root is between 86 and 87.
3
Pull out the biggest square factor: 7564 = 4 × 1891, so
$\sqrt{7564} = \sqrt{4 \times 1891} = 2\sqrt{1891}$
4
A calculator, or long division of digits, gives
$\sqrt{7564} \approx 86.97126$

LaTeX source of the formulas on this page

\[ \sqrt{7564} = 2\sqrt{1891} \approx 86.97126 \]
\[ \sqrt{7564} = \sqrt{4 \times 1891} = 2\sqrt{1891} \]
\[ \sqrt{7564} \approx 86.97126 \]

What is the square root of 7564?

The square root of 7564 is 86.97126 (rounded to 6 decimal places). In simplest radical form it is 2√1891.

Is 7564 a perfect square?

No. It lies between 86² = 7396 and 87² = 7569.

What is 7564 squared?

7564 × 7564 = 57214096.

What is the square root of 7564 rounded to 2 decimals?

86.97.