Question

square root of 75 over 2 + 3 square root of 2 over 4 =?

Answer 1

Is this the question?

\( \dfrac{\sqrt{75}}{2} + \dfrac{3 \sqrt{2}}{4} = \)

Answer 2

Yes.

Answer 3

You need to add two fractions.
What do two fractions that are to be added need to have?

Answer 4

Uh, Idk?

Answer 5

A common denominator.

Answer 6

The denominators are 2 and 4.
What is the LCD of 2 and 4?

Answer 7

2?

Answer 8

No. The LCD is the "least common denominator." That means the smallest number that you can divide by both numbers evenly (without remainder).

The LCD of 2 and 4 is 4, since 4 is the smallest number divisible by both 2 and 4.

Answer 9

The right fraction already has the LCD.
Now we need the LCD in the left fraction.

Answer 10

Okay

Answer 11

\(\dfrac{\sqrt{75}}{2} + \dfrac{3 \sqrt{2}}{4} =\)

\(=\dfrac{2}{2} \times \dfrac{\sqrt{75}}{2} + \dfrac{3 \sqrt{2}}{4} \)

\(=\dfrac{2\sqrt{75}}{4} + \dfrac{3 \sqrt{2}}{4} \)

Now that we have the same denominator, we can add the fractions.

Answer 12

alright.

Answer 13

Now we add the fractions.

Answer 14

how?

Answer 15

\(=\dfrac{2\sqrt{75}}{4} + \dfrac{3 \sqrt{2}}{4}\)

\(= \dfrac{ 2\sqrt{75} + 3 \sqrt{2}}{4}\)

Now we can do one final step.
We can simplify \(\sqrt{75} \).

Answer 16

\(= \dfrac{ 2\sqrt{25 \times 3} + 3 \sqrt{2}}{4}\)

\(= \dfrac{ 2\sqrt{25} \times \sqrt {3} + 3 \sqrt{2}}{4}\)

\(= \dfrac{ 2 \times 5\sqrt {3} + 3 \sqrt{2}}{4}\)

\(= \dfrac{ 10\sqrt {3} + 3 \sqrt{2}}{4}\)

Answer 17

How did you get that?

Answer 18

I did it step-by-step. Just go over it a few times until you understand it.