1 simplify the radical expression.

√50
a 5√2
b2√5
c5√10
d5

2 simplify the radical expression √180x^2

Somone should give the test answers

I will show you the first one ....

√50
= √25*√2
= 5√2

general method: Factor your number so that one or more factors are perfect squares.
e.g. √720 = √9*√16*√5
= 3*4*√5 = 12√5

Show me what you did for the 2nd question

1. Well, let's use some math tricks to simplify √50. We can break down 50 into its factors: 2 × 25. And since 25 is a perfect square, we know it simplifies to 5. So the answer is definitely not "d5" because a clown wouldn't make such a silly mistake.

Looking at the remaining options, we can see that we need to simplify the remaining factor of 2. So, we can write √50 as √(2 × 25), which further simplifies to √2 × √25. Since √25 is 5, we are left with 5√2.

Therefore, the correct answer would be a) 5√2.

2. Now let's tackle √180x^2. This time, we want to break down 180 into its prime factors: 2 × 2 × 3 × 3 × 5. Since we have x^2 within the square root, we can take one x out of the square root and leave one x inside.

So, we can simplify √180x^2 into 2 × 3x √5. And we all know that 2 × 3 is equal to 6. So, the final answer is 6x√5.

But don't worry if you don't understand math jokes, I'll always be here to assist you!

To simplify the radical expression √50, we can factor 50 into its prime factors. 50 can be factored as 2 × 5 × 5. Since there is a pair of 5's, they can be taken out of the square root. Taking them out, we have:

√50 = √(2 × 5 × 5) = 5√2

Therefore, the simplified form of √50 is 5√2. So, the correct answer is option a.

Now, let's simplify the radical expression √180x^2.

To simplify this expression, we need to find all the perfect square factors of 180. The prime factorization of 180 is 2 × 2 × 3 × 3 × 5. Notice that there are two pairs of 2's and one pair of 3's, so we can take them out of the square root:

√180x^2 = √(2 × 2 × 3 × 3 × 5 × x^2) = 2 × 3 × √(2 × 5 × x^2) = 6x√(2 × 5)

Therefore, the simplified form of √180x^2 is 6x√(2 × 5).

To simplify radical expressions, we want to break down the number inside the square root into its prime factors. Let's solve each problem step by step:

1. √50
To simplify, we need to find the prime factors of 50. We know that 50 can be written as 2 * 25. Now, let's break down 25 further: 25 can be further simplified as 5 * 5.
Combining these prime factors, we get √50 = √(2 * 5 * 5).

Simplifying further, we can bring out any pairs of like factors outside the square root. Here, we have two 5s. Therefore, we can rewrite this expression as √(2 * 5 * 5) = 5√2.

So, the answer is option (a) 5√2.

2. √180x^2
To simplify this expression, we need to break down both 180 and x^2 into their prime factors.
Let's start with 180: The prime factors of 180 are 2 * 2 * 3 * 3 * 5 = 2^2 * 3^2 * 5.
Now, looking at x^2, we have x * x = x^2.

Combining these prime factors with x^2, we get √(2^2 * 3^2 * 5 * x^2).

Next, we can bring out any pairs of like factors outside the square root. In this case, we have 2 * 3 * x. So, we can simplify this expression as √(2^2 * 3^2 * 5 * x^2) = 2 * 3 * x * √5 = 6x√5.

So, the answer is 6x√5.