Square root of 7972

The square root of 7972 is 89.286057 (rounded to 6 decimal places). In simplest radical form it is 2√1993.

Square root of 7972

Pick any whole number from 1 to 10,000.

\sqrt{7972} = 2\sqrt{1993} \approx 89.286057

How to work it out

1
The square root of 7972 is the number that multiplied by itself gives 7972.
2
7972 is between the perfect squares 89² = 7921 and 90² = 8100, so its square root is between 89 and 90.
3
Pull out the biggest square factor: 7972 = 4 × 1993, so
$\sqrt{7972} = \sqrt{4 \times 1993} = 2\sqrt{1993}$
4
A calculator, or long division of digits, gives
$\sqrt{7972} \approx 89.286057$

LaTeX source of the formulas on this page

\[ \sqrt{7972} = 2\sqrt{1993} \approx 89.286057 \]
\[ \sqrt{7972} = \sqrt{4 \times 1993} = 2\sqrt{1993} \]
\[ \sqrt{7972} \approx 89.286057 \]

What is the square root of 7972?

The square root of 7972 is 89.286057 (rounded to 6 decimal places). In simplest radical form it is 2√1993.

Is 7972 a perfect square?

No. It lies between 89² = 7921 and 90² = 8100.

What is 7972 squared?

7972 × 7972 = 63552784.

What is the square root of 7972 rounded to 2 decimals?

89.29.