Solve sqrt{60}+sqrt{105}*sqrt{45}+sqrt{147}

$$\sqrt { 60 } + \sqrt { 105 } \cdot \sqrt { 45 } + \sqrt { 147 }$$

Evaluate

$$2\sqrt{15}+7\sqrt{3}+15\sqrt{21}\approx 88.60895777$$

Solution Steps

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$2\sqrt{15}+\sqrt{105}\sqrt{45}+\sqrt{147}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$2\sqrt{15}+\sqrt{105}\times 3\sqrt{5}+\sqrt{147}$$

Factor 105=5\times 21. Rewrite the square root of the product \sqrt{5\times 21} as the product of square roots \sqrt{5}\sqrt{21}.

$$2\sqrt{15}+\sqrt{5}\sqrt{21}\times 3\sqrt{5}+\sqrt{147}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$2\sqrt{15}+5\times 3\sqrt{21}+\sqrt{147}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$2\sqrt{15}+5\times 3\sqrt{21}+7\sqrt{3}$$

Multiply 5 and 3 to get 15.

$$2\sqrt{15}+15\sqrt{21}+7\sqrt{3}$$