Solve a=15sqrt{2}:7sqrt{2}+3sqrt{8}:7sqrt{2}

$$a = 15 \sqrt { 2 } : 7 \sqrt { 2 } + 3 \sqrt { 8 } : 7 \sqrt { 2 }$$

Solve for a

$$a=6$$

Steps for Solving Linear Equation

Express \frac{15\sqrt{2}}{7}\sqrt{2} as a single fraction.

$$a=\frac{15\sqrt{2}\sqrt{2}}{7}+\frac{3\sqrt{8}}{7}\sqrt{2}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$a=\frac{15\sqrt{2}\sqrt{2}}{7}+\frac{3\times 2\sqrt{2}}{7}\sqrt{2}$$

Multiply 3 and 2 to get 6.

$$a=\frac{15\sqrt{2}\sqrt{2}}{7}+\frac{6\sqrt{2}}{7}\sqrt{2}$$

Express \frac{6\sqrt{2}}{7}\sqrt{2} as a single fraction.

$$a=\frac{15\sqrt{2}\sqrt{2}}{7}+\frac{6\sqrt{2}\sqrt{2}}{7}$$

Since \frac{15\sqrt{2}\sqrt{2}}{7} and \frac{6\sqrt{2}\sqrt{2}}{7} have the same denominator, add them by adding their numerators.

$$a=\frac{15\sqrt{2}\sqrt{2}+6\sqrt{2}\sqrt{2}}{7}$$

Do the multiplications in 15\sqrt{2}\sqrt{2}+6\sqrt{2}\sqrt{2}.

$$a=\frac{30+12}{7}$$

Do the calculations in 30+12.

$$a=\frac{42}{7}$$

Divide 42 by 7 to get 6.

$$a=6$$

Assign a

$$a≔6$$