simplify sqrt(10/18) — step-by-step solution

Let's simplify:

\sqrt{\frac{10}{18}}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

\frac{10}{18}

\frac{5 \times 2}{9 \times 2}

\frac{5}{9}

\sqrt{\frac{5}{9}}

ⓘ The root of a quotient is the quotient of the roots, sqrt(a/b) = sqrt(a)/sqrt(b):

\sqrt{\frac{5}{9}}

\frac{\sqrt{5}}{\sqrt{9}}

\frac{\sqrt{5}}{\sqrt{9}}

ⓘ The square root of a number is the positive number whose square is that number:

\sqrt{9}

3

;

3^{2}

9

▶Simplified form:

\frac{\sqrt{5}}{3}

The numeric value of:

\frac{\sqrt{5}}{3}

equals:

\frac{\approx 2.2361}{3}

▷

\approx 0.7454