Solve sqrt{21/4}*sqrt{(-2)^2}+sqrt{1-9/25}*sqrt{25}

$$\sqrt { 2 \frac { 1 } { 4 } } \times \sqrt { ( - 2 ) ^ { 2 } } + \sqrt { 1 - \frac { 9 } { 25 } } \times \sqrt { 25 }$$

Evaluate

$$7$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\sqrt{\frac{8+1}{4}}\sqrt{\left(-2\right)^{2}}+\sqrt{1-\frac{9}{25}}\sqrt{25}$$

Add 8 and 1 to get 9.

$$\sqrt{\frac{9}{4}}\sqrt{\left(-2\right)^{2}}+\sqrt{1-\frac{9}{25}}\sqrt{25}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{3}{2}\sqrt{\left(-2\right)^{2}}+\sqrt{1-\frac{9}{25}}\sqrt{25}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{3}{2}\sqrt{4}+\sqrt{1-\frac{9}{25}}\sqrt{25}$$

Calculate the square root of 4 and get 2.

$$\frac{3}{2}\times 2+\sqrt{1-\frac{9}{25}}\sqrt{25}$$

Cancel out 2 and 2.

$$3+\sqrt{1-\frac{9}{25}}\sqrt{25}$$

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

$$3+\sqrt{\frac{25}{25}-\frac{9}{25}}\sqrt{25}$$

Since \frac{25}{25} and \frac{9}{25} have the same denominator, subtract them by subtracting their numerators.

$$3+\sqrt{\frac{25-9}{25}}\sqrt{25}$$

Subtract 9 from 25 to get 16.

$$3+\sqrt{\frac{16}{25}}\sqrt{25}$$

Rewrite the square root of the division \frac{16}{25} as the division of square roots \frac{\sqrt{16}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$3+\frac{4}{5}\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$3+\frac{4}{5}\times 5$$

Cancel out 5 and 5.

$$3+4$$

Add 3 and 4 to get 7.

$$7$$

Factor

$$7$$