Square root of 147

The square root of 147 is 12.124356 (rounded to 6 decimal places). In simplest radical form it is 7√3.

Square root of 147

Pick any whole number from 1 to 10,000.

\sqrt{147} = 7\sqrt{3} \approx 12.124356

How to work it out

1
The square root of 147 is the number that multiplied by itself gives 147.
2
147 is between the perfect squares 12² = 144 and 13² = 169, so its square root is between 12 and 13.
3
Pull out the biggest square factor: 147 = 49 × 3, so
$\sqrt{147} = \sqrt{49 \times 3} = 7\sqrt{3}$
4
A calculator, or long division of digits, gives
$\sqrt{147} \approx 12.124356$

LaTeX source of the formulas on this page

\[ \sqrt{147} = 7\sqrt{3} \approx 12.124356 \]
\[ \sqrt{147} = \sqrt{49 \times 3} = 7\sqrt{3} \]
\[ \sqrt{147} \approx 12.124356 \]

What is the square root of 147?

The square root of 147 is 12.124356 (rounded to 6 decimal places). In simplest radical form it is 7√3.

Is 147 a perfect square?

No. It lies between 12² = 144 and 13² = 169.

What is 147 squared?

147 × 147 = 21609.

What is the square root of 147 rounded to 2 decimals?

12.12.