Could someone show me how to solve these problems step by step....
I am confused on how to fully break this down to simpliest terms
sqrt 3 * sqrt 15=
sqrt 6 * sqrt 8 =
sqrt 20 * sqrt 5 =
since both terms are sqrt , you can combine them.
sqrt 3* sqrt 15= sqrt (15*3)= sqrt 45
sqrt 6* sqrt8 = sqrt (6*8)= sqrt 48
sqrt 20* sqrt5= sqrt (20*5)= sqrt 100
sqrt 3 * sqrt 15= sqrt 3 *sqrt 3 * sqrt 5
= 3*sqrt5
similarly sqrt 6 * sqrt 8 = 4sqrt3
and sqrt 20 * sqrt 5 = 10
To solve these problems step by step:
1. Let's start with the first problem:
sqrt(3) * sqrt(15)
Since both terms are square roots, we can combine them into a single square root.
Multiplying the values inside the square root:
sqrt(3 * 15)
Simplifying the multiplication inside:
sqrt(45)
The square root of 45 cannot be simplified further, so the final answer is:
sqrt(45)
2. Moving on to the second problem:
sqrt(6) * sqrt(8)
Again, we combine the square roots into a single square root:
sqrt(6 * 8)
Simplifying the multiplication inside:
sqrt(48)
To simplify further, let's look for perfect squares that can be factored out.
Since 48 = 16 * 3, we can rewrite it as:
sqrt(16 * 3)
Taking the square root of 16:
sqrt(16) * sqrt(3)
Since the square root of 16 is 4, we have:
4 * sqrt(3)
The final answer is:
4 * sqrt(3)
3. Lastly, let's solve the third problem:
sqrt(20) * sqrt(5)
Combining the square roots into a single square root:
sqrt(20 * 5)
Simplifying the multiplication inside:
sqrt(100)
The square root of 100 is 10, so the final answer is:
10
So, the fully simplified expressions are:
1. sqrt(45)
2. 4 * sqrt(3)
3. 10