Answer:
<span>=3<span>√6</span>−3<span>√5</span></span>
Explanation:
<span>3<span><span>√5</span>+<span>√6</span></span></span>
We rationalise the denominator by multiplying the expression by the conjugate of the denominator. <span><span>√5</span>−<span>√6</span></span>
<span><span>3⋅<span>(<span>√5</span>−<span>√6</span>)</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span>
<span>=<span><span>3⋅<span>(<span>√5</span>)</span>+3⋅<span>(−<span>√6</span>)</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span></span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span></span>
<span>Applying identity
<span><span>(a+b)</span><span>(a−b)</span>=<span>a2</span>−<span>b2</span></span> to the denominator.</span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span><span><span>(<span>√5</span>)</span>2</span>−<span><span>(<span>√6</span>)</span>2</span></span></span></span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span>5−6</span></span></span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span>−1</span></span></span>
<span>=−3<span>√5</span>+3<span>√6</span></span>
<span>=3<span>√6</span>−3<span>√<span>5
</span></span></span>
Answer:
13) 
⇒ ![\frac{1}{\sqrt[4]{(5x)^5}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%5B4%5D%7B%285x%29%5E5%7D%7D)
15) 
⇒ 
Step-by-step explanation:
Given expression:
13)
15)
Write the expressions in radical form.
Solution:
For an expression with exponents as fraction like
the numerator 
represents the power it is raised to and the denominator 
represents the nth root of the expression.
For an expression with exponents as negative fraction like
We take the reciprocal of the term by rule for negative exponents.
So it is written as:
using the above properties we can write the given expressions in radical form.
13)
⇒ 
[Using rule of negative exponents]
⇒ [writing in radical form]
15)
⇒ [Since 2nd root is given as 
in radical form]
Answer: He sold 10 pounds of cashews .
Step-by-step explanation:
Since we have given that
Selling price of walnuts = $4.00 a pound
Selling price of cashews = $7.00 a pound
Number of pounds of walnuts = 10
Let number of pounds of cashew be x
Total price at which he sold a mixture = $5.50
According to question,
Hence, he sold 10 pounds of cashews .
