Solve sqrt{(52*29)^2+(22*98)^2+(1*5^2)}

$$\sqrt { ( 52 \cdot 29 ) ^ { 2 } + ( 22 \cdot 98 ) ^ { 2 } + ( 1 \cdot 5 ^ { 2 } ) }$$

Evaluate

$$5\sqrt{276897}\approx 2631.050170559$$

Solution Steps

Multiply 52 and 29 to get 1508.

$$\sqrt{1508^{2}+\left(22\times 98\right)^{2}+1\times 5^{2}}$$

Calculate 1508 to the power of 2 and get 2274064.

$$\sqrt{2274064+\left(22\times 98\right)^{2}+1\times 5^{2}}$$

Multiply 22 and 98 to get 2156.

$$\sqrt{2274064+2156^{2}+1\times 5^{2}}$$

Calculate 2156 to the power of 2 and get 4648336.

$$\sqrt{2274064+4648336+1\times 5^{2}}$$

Add 2274064 and 4648336 to get 6922400.

$$\sqrt{6922400+1\times 5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{6922400+1\times 25}$$

Multiply 1 and 25 to get 25.

$$\sqrt{6922400+25}$$

Add 6922400 and 25 to get 6922425.

$$\sqrt{6922425}$$

Factor 6922425=5^{2}\times 276897. Rewrite the square root of the product \sqrt{5^{2}\times 276897} as the product of square roots \sqrt{5^{2}}\sqrt{276897}. Take the square root of 5^{2}.

$$5\sqrt{276897}$$