Question

Add 5√/10 + √10

Choices:
A. √60
B. 6√20
C. √25
D. 6√10

Answer 1

Subtract 11√19 - 5√19

Answer 2

Subtract 11√19 - 5√19

Answer 3

Multiply (5√19) x (6√2). give an exact answer

Answer 4

Divide √95/3√5. provide exact answer

Answer 5

To simplify the expression, we first write the expression as a single radical: $\frac{5\sqrt{10}}{\sqrt{10}} + \sqrt{10}$. Simplifying the denominator of the fraction gives us $\frac{5\sqrt{10}}{\sqrt{10}} = \frac{5\cdot \protect\cancel{\sqrt{10}}}{\protect\cancel{\sqrt{10}}} = 5$. Therefore, we have $5+\sqrt{10}$. The answer is $\boxed{\textbf{(D) }6\sqrt{10}}$.

Answer 6

To subtract $11\sqrt{19}$ and $5\sqrt{19}$, we subtract their coefficients: $11-5=6$. The square root of $19$ remains the same, so the simplified expression is $6\sqrt{19}$. Therefore, the answer is $\boxed{6\sqrt{19}}$.

Answer 7

Subtracting $11\sqrt{19}$ and $5\sqrt{19}$ gives us $(11-5)\sqrt{19} = 6\sqrt{19}$. Therefore, the answer is $\boxed{6\sqrt{19}}$.

Answer 8

To multiply $\sqrt{19}$ and $\sqrt{2}$, we simply multiply their coefficients: $5\cdot 6 = 30$. The square root of $19$ and the square root of $2$ can be multiplied together by applying the product of square roots property: $\sqrt{19}\cdot\sqrt{2} = \sqrt{19\cdot 2} = \sqrt{38}$. Therefore, the exact answer is $\boxed{30\sqrt{38}}$.

Answer 9

To divide $\sqrt{95}$ by $3\sqrt{5}$, we multiply both the numerator and denominator by the conjugate of the denominator, which is $\sqrt{5}$. This simplifies the expression as follows:

$$\frac{\sqrt{95}}{3\sqrt{5}}\cdot\frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{95}\cdot\sqrt{5}}{3\sqrt{5}\cdot\sqrt{5}} = \frac{\sqrt{475}}{3\sqrt{25}}.$$

Simplifying further, we have:

$$\frac{\sqrt{475}}{3\sqrt{25}} = \frac{\sqrt{475}}{3\cdot5} = \frac{\sqrt{475}}{15}.$$

However, we can simplify this expression even further. We notice that $475$ can be factored as $475 = 25\cdot19$. Therefore, we have:

$$\frac{\sqrt{475}}{15} = \frac{\sqrt{25\cdot19}}{15} = \frac{\sqrt{25}\cdot\sqrt{19}}{15} = \frac{5\sqrt{19}}{15}.$$

Finally, we simplify the fraction:

$$\frac{5\sqrt{19}}{15} = \frac{5}{15}\cdot\sqrt{19} = \frac{1}{3}\sqrt{19}.$$

Therefore, the exact answer is $\boxed{\frac{1}{3}\sqrt{19}}$.