Question

Simplify √28 . √27 . √5

Simplify 2√5 + 3√5 - √5

Which expression is equal to 2√28 - 5√63

A) -√7
B) -37√7
C) √7
D) -11√7

Thank you

Answer 1

Answer:

1. 6√105

2. 4√5

3. D

Step-by-step explanation:

Math is an interesting invention.

Answer 2

Answer:

Simplify $\sqrt{28} \times \sqrt{27} \times \sqrt{5}$

Observe that all roots are similar, because they are square roots.

To simplify this products, we can write only one root and multiply all sub-radical numbers, as follows

$\sqrt{28} \times \sqrt{27} \times \sqrt{5}=\sqrt{28 \times 27 \times 5}$

It's better to maintain the product as factors, so, let's express each number in a power

$\sqrt{28} \times \sqrt{27} \times \sqrt{5}=\sqrt{28 \times 27 \times 5}=\sqrt{2^{2} \times 7 \times 3^{2} \times 3 \times 5 }$

Then, all square powers can go out the root

$\sqrt{2^{2} \times 7 \times 3^{2} \times 3 \times 5 }=2\times 3 \sqrt{105}=6 \sqrt{105}$

Therefore, the answer here is $6\sqrt{105}$

Simplify $2\sqrt{5}+3\sqrt{5}-\sqrt{5}$

Observe that all roots are exactly the same, we proceed to sum and subtract the whole part of each term

$2\sqrt{5}+3\sqrt{5}-\sqrt{5}=(2+3-1)\sqrt{5}=4\sqrt{5}$

Therefore, the answer is $4\sqrt{5}$

Which expression is equal to $2\sqrt{28}-5\sqrt{63}$

Let's express each root in factors

$2\sqrt{28}-5\sqrt{63}=2\sqrt{7 \times 4} -5 \sqrt{7 \times 9}$

Then, we solve the root for 4 and 9

$2\sqrt{7 \times 4} -5 \sqrt{7 \times 9}=4\sqrt{7}-15\sqrt{7}$

Then, we subtract

$4\sqrt{7}-15\sqrt{7}=-11\sqrt{7}$

Therefore, the right answer is D.