Simplify the expression, 4√18 + 5√32.
A: 45√2
B: 32√2
C: 116√2
D: 9√50
D: 9√50
To simplify the expression, we first need to simplify √18 and √32:
√18 = √(2*9) = 3√2
√32 = √(2*16) = 4√2
Now, we substitute these back into the original expression:
4√18 + 5√32
= 4(3√2) + 5(4√2)
= 12√2 + 20√2
= 32√2
So, the simplified expression is 32√2, which corresponds to option B.
Simplify the expression, 7√5 - 3√80.
A: -5√5
B: -4√75
C: -5
D: 4√-75
Simplify the expression, 7√5 - 3√80.
First, simplify √80:
√80 = √(16*5) = 4√5
Now substitute this back into the original expression:
7√5 - 3(4√5) = 7√5 - 12√5 = -5√5
Therefore, the simplified expression is -5√5, which corresponds to option A.
Simplify the expression, √21(√3+√14).
A: 9√7 - 49√6
B: 2√6 + √35
C: 3√7 + 7√6
D: √357
To simplify the given expression √21(√3+√14), we will use the distributive property:
√21(√3+√14) = √21 * √3 + √21 * √14
= √(21 * 3) + √(21 * 14)
= √63 + √294
Now, we simplify the square roots:
√63 = √(9 * 7) = 3√7
√294 = √(42 * 7) = √42 * √7 = 2√7 * √7 = 2√7^2 = 14
Substitute back into the expression:
√21(√3+√14) = 3√7 + 14
Therefore, the simplified expression is 3√7 + 14, which corresponds to option C.
Please simplify by rationalizing the denominator 4/√10 - √6.
A: √10 + √6
B: 4
C: 4√10 + 4√6
D: 4√10 - 4√6/16 - 2√15
To rationalize the denominator of the expression 4/√10 - √6, we need to get rid of the square root in the denominator.
First, we will rationalize the denominator:
4/√10 - √6 can be written as (4√10 - √6√10)/(√10)
This simplifies to (4√10 - √60)/(√10) since √6√10 = √60.
To simplify further, we can divide each term on the numerator by √10:
(4√10/√10 - √60/√10)
= 4 - √6√10
Therefore, the expression 4/√10 - √6, when simplified and rationalized, is 4 - √6√10 which corresponds to option B.
Simplify 2/√5
A: 2/√5
B: √10
C: (√10)/5
D: (2√5/)5
To simplify 2/√5, we can rationalize the denominator by multiplying both the numerator and denominator by √5:
(2/√5) * (√5/√5)
= 2√5/5
Therefore, 2/√5 simplifies to 2√5/5, which corresponds to option D.
Please simplify -11√112.
A: -44√7
B: -176√7
C: -27√7
D: 4√7