Simplify the following expressions: 8. 12 extsqrt(17) − 8 extsqrt(17) 9. 5 extsqrt(5) + extsqrt(5) 10. 5…

Question

Simplify the following expressions: 8. 12 extsqrt(17) − 8 extsqrt(17) 9. 5 extsqrt(5) + extsqrt(5) 10. 5 extsqrt(7) × (2/5) extsqrt(7) 11. (3 extsqrt(2))2

ScanSolve AI Tutor · Accepted Answer

here are the solutions for problems 8, 9, 10, and 11:

8. $12\sqrt{17} - 8\sqrt{17}$

Identify the common surd.
Both terms have $\sqrt{17}$ .
Factor out the common surd.
$(12 - 8)\sqrt{17}$
Perform the subtraction.
$4\sqrt{17}$
The simplified expression is:
$\boxed{4\sqrt{17}}$
9. $5\sqrt{5} + \sqrt{5}$
Identify the common surd.
Both terms have $\sqrt{5}$ . Note that $\sqrt{5}$ is equivalent to $1\sqrt{5}$ .
Factor out the common surd.
$(5 + 1)\sqrt{5}$
Perform the addition.
$6\sqrt{5}$
The simplified expression is:
$\boxed{6\sqrt{5}}$
10. $5\sqrt{7} \times \frac{2}{5}\sqrt{7}$
Group the numerical coefficients and the surds.
$\left(5 \times \frac{2}{5}\right) \times (\sqrt{7} \times \sqrt{7})$
Multiply the numerical coefficients.
$5 \times \frac{2}{5} = \frac{10}{5} = 2$
Multiply the surds.
Recall that $\sqrt{a} \times \sqrt{a} = a$ .
$\sqrt{7} \times \sqrt{7} = 7$
Multiply the results from Step 2 and Step 3.
$2 \times 7 = 14$
The evaluated expression is:
$\boxed{14}$
11. Simplify by expressing $(3\sqrt{2})^2$ as a complete surd.
Apply the exponent to both parts inside the parenthesis.
Recall that $(ab)^n = a^n b^n$ .
$(3\sqrt{2})^2 = 3^2 \times (\sqrt{2})^2$
Evaluate each part.
$3^2 = 9$ $(\sqrt{2})^2 = 2$
Multiply the results.
$9 \times 2 = 18$
Express the result as a complete surd.
To express 18 as a complete surd, we need to write it as $\sqrt{x}$ .
$18 = \sqrt{18^2} = \sqrt{324}$
The expression as a complete surd is:
$\boxed{\sqrt{324}}$

Simplify the following expressions: 8. 12 extsqrt(17) - 8 extsqrt(17) 9. 5 extsqrt(5) + extsqrt(5) 10. 5 extsqrt(7) * (2/5) extsqrt(7) 11. (3 extsqrt(2))2

Step-by-step solution

Identify the common surd.

Factor out the common surd.

Perform the subtraction.

Identify the common surd.

Factor out the common surd.

Perform the addition.

Group the numerical coefficients and the surds.

Multiply the numerical coefficients.

Multiply the surds.

Multiply the results from Step 2 and Step 3.

Apply the exponent to both parts inside the parenthesis.

Evaluate each part.

Multiply the results.

Express the result as a complete surd.

Still stuck on this one?

More Mathematics Questions