Solve sqrt{(3*5)^2+(4-7)^2}

$$\sqrt { ( 3 \times 5 ) ^ { 2 } + ( 4 - 7 ) ^ { 2 } }$$

Evaluate

$$3\sqrt{26}\approx 15.297058541$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\sqrt{15^{2}+\left(4-7\right)^{2}}$$

Calculate 15 to the power of 2 and get 225.

$$\sqrt{225+\left(4-7\right)^{2}}$$

Subtract 7 from 4 to get -3.

$$\sqrt{225+\left(-3\right)^{2}}$$

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

$$\sqrt{225+9}$$

Add 225 and 9 to get 234.

$$\sqrt{234}$$

Factor 234=3^{2}\times 26. Rewrite the square root of the product \sqrt{3^{2}\times 26} as the product of square roots \sqrt{3^{2}}\sqrt{26}. Take the square root of 3^{2}.

$$3\sqrt{26}$$