Simplify the expressions and solve the equations

1. 2√3 - √12

My answer: 2√3 - 2√3 = 0

2. √(5p + 5)^2 = √(6p + )^2

I got the answer p = 4

3. √(28) + √(63) + √(175)

This one seems so simple. I tried multiple times, but I can't seem to get the correct answer. I think i'm making some little mistake in the calculations or something.

4. √(2w + 5) + 4 = √(25)

My answer: -3.5

5. √(18)/√(8 - 3)

My answer: -12 - 9 √2

#1 ok

#2 ok if you meant √(6p+1)

#3
√28 + √63 + √175
2√7 + 3√7 + 5√7 = 10√7

#4
√(2w+5) + 4 = √25
√(2w+5) = 1
2w+5 = 1
2w = -4
w = -2

#5
√18/√(8-3)
3√2 / √5
(3√10)/5

If you meant

√18/(√8-3)
(3√2)(√8+3)/5
(12+9√2)/5
How did you come up with your answer?

I have a question.

#3: On my calculator, √28 + √63 + √175 = 6.06, but 10√7 = 26.5. Shouldn't they = the same number?

As for #5.. I'm not really sure, tbh. I tried that problem a while a go and I'm not quite sure where I was going with it.

There's no way that

√28 + √63 + √175 = 6.06

You must have hit some wrong keys

Just a rough approximation would be

5 + 8 + 13 = 26, not 6.06!

Well, I entered in the calculator √28 + √63 + √175 and got 6.06. I just entered the expression. I didn't take the sq roots first.

1. To simplify the expression 2√3 - √12, we can start by simplifying the square roots. √12 can be broken down into √(4 * 3), which simplifies to 2√3. Now the expression becomes 2√3 - 2√3. Since both terms are the same, when we subtract them, the result is 0.

2. To solve the equation √(5p + 5)^2 = √(6p + )^2, we need to remove the square roots. We can square both sides of the equation to simplify it. (√(5p + 5))^2 simplifies to 5p + 5, and (√(6p + )^2) simplifies to 6p +. Now the equation becomes 5p + 5 = 6p +. Rearranging the equation, we get p = 4.

3. To simplify the expression √(28) + √(63) + √(175), we need to simplify each square root separately.

√(28) can be broken down into √(4 * 7), which simplifies to 2√7.
√(63) can be broken down into √(9 * 7), which simplifies to 3√7.
√(175) can be broken down into √(25 * 7), which simplifies to 5√7.

Now, the expression becomes 2√7 + 3√7 + 5√7. We can combine like terms, so the final result is 10√7.

4. To solve the equation √(2w + 5) + 4 = √(25), we need to isolate the variable w.

First, let's solve for √(2w + 5). Subtract 4 from both sides of the equation:

√(2w + 5) = √(25) - 4

√(2w + 5) = 5 - 4

√(2w + 5) = 1

Now, square both sides of the equation to eliminate the square root:

(√(2w + 5))^2 = 1^2

2w + 5 = 1

Subtract 5 from both sides:

2w = 1 - 5

2w = -4

Finally, divide both sides by 2:

w = -4/2

w = -2

So, the solution to the equation is w = -2.

5. To simplify the expression √(18)/√(8 - 3), we need to simplify each square root separately and then perform the division.

√(18) can be broken down into √(9 * 2), which simplifies to 3√2.
√(8 - 3) simplifies to √5.

Now, the expression becomes (3√2)/(√5). To simplify the division of square roots, we multiply both the numerator and the denominator by the conjugate of the denominator:

[(3√2)/(√5)] * [√5/√5] = (3√10)/(√(5*5)) = (3√10)/5 = (3/5)√10

So, the simplified expression is (3/5)√10.