Square root of 7000

The square root of 7000 is 83.666003 (rounded to 6 decimal places). In simplest radical form it is 10√70.

Square root of 7000

Pick any whole number from 1 to 10,000.

\sqrt{7000} = 10\sqrt{70} \approx 83.666003

How to work it out

1
The square root of 7000 is the number that multiplied by itself gives 7000.
2
7000 is between the perfect squares 83² = 6889 and 84² = 7056, so its square root is between 83 and 84.
3
Pull out the biggest square factor: 7000 = 100 × 70, so
$\sqrt{7000} = \sqrt{100 \times 70} = 10\sqrt{70}$
4
A calculator, or long division of digits, gives
$\sqrt{7000} \approx 83.666003$

LaTeX source of the formulas on this page

\[ \sqrt{7000} = 10\sqrt{70} \approx 83.666003 \]
\[ \sqrt{7000} = \sqrt{100 \times 70} = 10\sqrt{70} \]
\[ \sqrt{7000} \approx 83.666003 \]

What is the square root of 7000?

The square root of 7000 is 83.666003 (rounded to 6 decimal places). In simplest radical form it is 10√70.

Is 7000 a perfect square?

No. It lies between 83² = 6889 and 84² = 7056.

What is 7000 squared?

7000 × 7000 = 49000000.

What is the square root of 7000 rounded to 2 decimals?

83.67.