Solve sqrt{64}+2sqrt{(-3)^2}-7sqrt{1,69}+3sqrt{25/16}

$$\sqrt { 64 } + 2 \sqrt { ( - 3 ) ^ { 2 } } - 7 \sqrt { 1,69 } + 3 \sqrt { \frac { 25 } { 16 } }$$

Evaluate

$$8,65$$

Solution Steps

Calculate the square root of 64 and get 8.

$$8+2\sqrt{\left(-3\right)^{2}}-7\sqrt{1,69}+3\sqrt{\frac{25}{16}}$$

Calculate -3 to the power of 2 and get 9.

$$8+2\sqrt{9}-7\sqrt{1,69}+3\sqrt{\frac{25}{16}}$$

Calculate the square root of 9 and get 3.

$$8+2\times 3-7\sqrt{1,69}+3\sqrt{\frac{25}{16}}$$

Multiply 2 and 3 to get 6.

$$8+6-7\sqrt{1,69}+3\sqrt{\frac{25}{16}}$$

Add 8 and 6 to get 14.

$$14-7\sqrt{1,69}+3\sqrt{\frac{25}{16}}$$

Calculate the square root of 1,69 and get 1,3.

$$14-7\times 1,3+3\sqrt{\frac{25}{16}}$$

Multiply -7 and 1,3 to get -9,1.

$$14-9,1+3\sqrt{\frac{25}{16}}$$

Subtract 9,1 from 14 to get 4,9.

$$4,9+3\sqrt{\frac{25}{16}}$$

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

$$4,9+3\times \frac{5}{4}$$

Express 3\times \frac{5}{4} as a single fraction.

$$4,9+\frac{3\times 5}{4}$$

Multiply 3 and 5 to get 15.

$$4,9+\frac{15}{4}$$

Convert decimal number 4,9 to fraction \frac{49}{10}.

$$\frac{49}{10}+\frac{15}{4}$$

Least common multiple of 10 and 4 is 20. Convert \frac{49}{10} and \frac{15}{4} to fractions with denominator 20.

$$\frac{98}{20}+\frac{75}{20}$$

Since \frac{98}{20} and \frac{75}{20} have the same denominator, add them by adding their numerators.

$$\frac{98+75}{20}$$

Add 98 and 75 to get 173.

$$\frac{173}{20}$$

Factor

$$\frac{173}{5 \cdot 2 ^ {2}} = 8\frac{13}{20} = 8.65$$