Solve sqrt{3^2*5^2}=sqrt{3^2}sqrt{5^2}

$$\sqrt { 3 ^ { 2 } \times 5 ^ { 2 } } = \sqrt { 3 ^ { 2 } } \sqrt { 5 ^ { 2 } }$$

Verify

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9\times 5^{2}}=\sqrt{3^{2}}\sqrt{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{9\times 25}=\sqrt{3^{2}}\sqrt{5^{2}}$$

Multiply 9 and 25 to get 225.

$$\sqrt{225}=\sqrt{3^{2}}\sqrt{5^{2}}$$

Calculate the square root of 225 and get 15.

$$15=\sqrt{3^{2}}\sqrt{5^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$15=\sqrt{9}\sqrt{5^{2}}$$

Calculate the square root of 9 and get 3.

$$15=3\sqrt{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$15=3\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$15=3\times 5$$

Multiply 3 and 5 to get 15.

$$15=15$$

Compare 15 and 15.

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