Solve sqrt{56}56sqrt{56+36}63/69

$$\sqrt{ 56 } 56 \sqrt{ 56+36 } \frac{ 63 }{ 69 }$$

Evaluate

$$\frac{4704\sqrt{322}}{23}\approx 3670.011396736$$

Solution Steps

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$56\times 2\sqrt{14}\sqrt{56+36}\times \frac{63}{69}$$

Multiply 56 and 2 to get 112.

$$112\sqrt{14}\sqrt{56+36}\times \frac{63}{69}$$

Add 56 and 36 to get 92.

$$112\sqrt{14}\sqrt{92}\times \frac{63}{69}$$

Factor 92=2^{2}\times 23. Rewrite the square root of the product \sqrt{2^{2}\times 23} as the product of square roots \sqrt{2^{2}}\sqrt{23}. Take the square root of 2^{2}.

$$112\sqrt{14}\times 2\sqrt{23}\times \frac{63}{69}$$

Multiply 112 and 2 to get 224.

$$224\sqrt{14}\sqrt{23}\times \frac{63}{69}$$

Reduce the fraction \frac{63}{69} to lowest terms by extracting and canceling out 3.

$$224\sqrt{14}\sqrt{23}\times \frac{21}{23}$$

Express 224\times \frac{21}{23} as a single fraction.

$$\frac{224\times 21}{23}\sqrt{14}\sqrt{23}$$

Multiply 224 and 21 to get 4704.

$$\frac{4704}{23}\sqrt{14}\sqrt{23}$$

To multiply \sqrt{14} and \sqrt{23}, multiply the numbers under the square root.

$$\frac{4704}{23}\sqrt{322}$$