Solve sqrt{80}quadsqrt{48}quadsqrt{75}quadsqrt{76}

$$\sqrt { 80 } \quad \sqrt { 48 } \quad \sqrt { 75 } \quad \sqrt { 76 }$$

Evaluate

$$480\sqrt{95}\approx 4678.461285508$$

Solution Steps

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$4\sqrt{5}\sqrt{48}\sqrt{75}\sqrt{76}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$4\sqrt{5}\times 4\sqrt{3}\sqrt{75}\sqrt{76}$$

Multiply 4 and 4 to get 16.

$$16\sqrt{5}\sqrt{3}\sqrt{75}\sqrt{76}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$16\sqrt{5}\sqrt{3}\times 5\sqrt{3}\sqrt{76}$$

Multiply 16 and 5 to get 80.

$$80\sqrt{5}\sqrt{3}\sqrt{3}\sqrt{76}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$80\sqrt{5}\times 3\sqrt{76}$$

Factor 76=2^{2}\times 19. Rewrite the square root of the product \sqrt{2^{2}\times 19} as the product of square roots \sqrt{2^{2}}\sqrt{19}. Take the square root of 2^{2}.

$$80\sqrt{5}\times 3\times 2\sqrt{19}$$

Multiply 80 and 2 to get 160.

$$160\sqrt{5}\times 3\sqrt{19}$$

Multiply 160 and 3 to get 480.

$$480\sqrt{5}\sqrt{19}$$

To multiply \sqrt{5} and \sqrt{19}, multiply the numbers under the square root.

$$480\sqrt{95}$$