Solve sqrt{1-16/25}=1-4/5

$$\sqrt { 1 - \frac { 16 } { 25 } } = 1 - \frac { 4 } { 5 }$$

Verify

Solution Steps

Convert 1 to fraction \frac{25}{25}.

$$\sqrt{\frac{25}{25}-\frac{16}{25}}=1-\frac{4}{5}$$

Since \frac{25}{25} and \frac{16}{25} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{25-16}{25}}=1-\frac{4}{5}$$

Subtract 16 from 25 to get 9.

$$\sqrt{\frac{9}{25}}=1-\frac{4}{5}$$

Rewrite the square root of the division \frac{9}{25} as the division of square roots \frac{\sqrt{9}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{3}{5}=1-\frac{4}{5}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{3}{5}=\frac{5}{5}-\frac{4}{5}$$

Since \frac{5}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{5}=\frac{5-4}{5}$$

Subtract 4 from 5 to get 1.

$$\frac{3}{5}=\frac{1}{5}$$

Compare \frac{3}{5} and \frac{1}{5}.

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