Solve sqrt{45div3-12div4}+sqrt{(1+21div3)*(1+25div5)}=

$$\sqrt{ 45 \div 3-12 \div 4 } + \sqrt{ (1+21 \div 3) \times (1+25 \div 5) } =$$

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

Divide 45 by 3 to get 15.

$$\sqrt{15-\frac{12}{4}}+\sqrt{\left(1+\frac{21}{3}\right)\left(1+\frac{25}{5}\right)}$$

Divide 12 by 4 to get 3.

$$\sqrt{15-3}+\sqrt{\left(1+\frac{21}{3}\right)\left(1+\frac{25}{5}\right)}$$

Subtract 3 from 15 to get 12.

$$\sqrt{12}+\sqrt{\left(1+\frac{21}{3}\right)\left(1+\frac{25}{5}\right)}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\sqrt{3}+\sqrt{\left(1+\frac{21}{3}\right)\left(1+\frac{25}{5}\right)}$$

Divide 21 by 3 to get 7.

$$2\sqrt{3}+\sqrt{\left(1+7\right)\left(1+\frac{25}{5}\right)}$$

Add 1 and 7 to get 8.

$$2\sqrt{3}+\sqrt{8\left(1+\frac{25}{5}\right)}$$

Divide 25 by 5 to get 5.

$$2\sqrt{3}+\sqrt{8\left(1+5\right)}$$

Add 1 and 5 to get 6.

$$2\sqrt{3}+\sqrt{8\times 6}$$

Multiply 8 and 6 to get 48.

$$2\sqrt{3}+\sqrt{48}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$2\sqrt{3}+4\sqrt{3}$$

Combine 2\sqrt{3} and 4\sqrt{3} to get 6\sqrt{3}.

$$6\sqrt{3}$$