Solve sqrt{52}sqrt{50}*sqrt{26}

$$\sqrt{ 52 } \sqrt{ 50 } \times \sqrt{ 26 }$$

Evaluate

$$260$$

Solution Steps

Factor 52=26\times 2. Rewrite the square root of the product \sqrt{26\times 2} as the product of square roots \sqrt{26}\sqrt{2}.

$$\sqrt{26}\sqrt{2}\sqrt{50}\sqrt{26}$$

Multiply \sqrt{26} and \sqrt{26} to get 26.

$$26\sqrt{50}\sqrt{2}$$

Factor 50=2\times 25. Rewrite the square root of the product \sqrt{2\times 25} as the product of square roots \sqrt{2}\sqrt{25}.

$$26\sqrt{2}\sqrt{25}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$26\times 2\sqrt{25}$$

Multiply 26 and 2 to get 52.

$$52\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$52\times 5$$

Multiply 52 and 5 to get 260.

$$260$$

Factor

$$2^{2}\times 5\times 13$$