When there is a radical by itself in the denominator, you multiply numerator and denominator by a radical that results in the product being rational. For a square root, that will usually be the same square root:

$\dfrac{9}{\sqrt{3}}=\dfrac{9}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{9\sqrt{3}}{3}=\boxed{3\sqrt{3}}$

If the problem has a sum in the denominator involving a square root, then you multiply numerator and denominator by the conjugate of that sum (the sum with the sign changed). This uses the special product "difference of squares" to eliminate the radical term.

<u>Example</u>:

$\dfrac{9}{2-\sqrt{3}}=\dfrac{9}{2-\sqrt{3}}\cdot\dfrac{2+\sqrt{3}}{2+\sqrt{3}}=\dfrac{9(2+\sqrt{3})}{2^2-(\sqrt{3})^2}=\dfrac{18+9\sqrt{3}}{4-3}\\\\=\boxed{18+9\sqrt{3}}$

It is easy to demonstrate that none of the offered choices for this problem has the same value as 9/√3.

9/√3 ≈ 5.196. Offered choices have values of about 4.798, 1.732, 6.681, 23.196 -- none even close.

Please discuss this question with your teacher.

3 0

3 years ago

Dana and her 4 friends are going on a camping trip. Dana wants to see how much fruit she can share so everyone will get the same

kupik [55]

I agree that the answer is 6. 30÷5=6

6 0

4 years ago

3+6×5+4÷2-7 using the same expression,add parentheses so that the value of the expression is 38

solmaris [256]

Answer:

3+6×(5+4÷2)-7

Step-by-step explanation:

To solve the expression use order of operations.

Right now the expression solves to:

3+6×5+4÷2-7 6* 5 = 30

3 + 30 + 4÷2-7 4 ÷ 2 = 2

3 + 30 + 2 - 7 Add and subtract left to right.

33 + 2 - 7

35 - 7

To make it solve to 38, add parenthesis:

3+6×(5+4÷2)-7 (5+4÷2) = 7

3+6×(7)-7 6*7 = 42

3 + 42 - 7 Add and subtract from left to right

45 - 7

7 0

3 years ago