Solve sqrt{5}sqrt[4]{9}sqrt[4]{49}

$$\sqrt{ 5 } \sqrt[ 4 ]{ 9 } \sqrt[ 4 ]{ 49 }$$

Evaluate

$$\sqrt{105}\approx 10.246950766$$

Solution Steps

Rewrite \sqrt[4]{9} as \sqrt[4]{3^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[4]{9}=\sqrt[4]{3^{2}}=3^{\frac{2}{4}}=3^{\frac{1}{2}}=\sqrt{3}$$

Insert the obtained value back in the expression.

$$\sqrt{5}\sqrt{3}\sqrt[4]{49}$$

Rewrite \sqrt[4]{49} as \sqrt[4]{7^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[4]{49}=\sqrt[4]{7^{2}}=7^{\frac{2}{4}}=7^{\frac{1}{2}}=\sqrt{7}$$

Insert the obtained value back in the expression.

$$\sqrt{5}\sqrt{3}\sqrt{7}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\sqrt{15}\sqrt{7}$$

To multiply \sqrt{15} and \sqrt{7}, multiply the numbers under the square root.

$$\sqrt{105}$$