Simplify: sqrt (21) (sqrt(7) + sqrt(3))
a) 7 sqrt (3) + 3 sqrt(7)
b) 7 sqrt(3) + sqrt (3)
c) sqrt (210)
d) sqrt (147) + sqrt (63)''.
a
thanks reiny
To simplify the expression sqrt(21)(sqrt(7) + sqrt(3)), we can use the distributive property.
First, distribute sqrt(21) to both terms inside the parentheses:
sqrt(21) * sqrt(7) = sqrt(21 * 7) = sqrt(147)
sqrt(21) * sqrt(3) = sqrt(21 * 3) = sqrt(63)
So, the simplified expression becomes sqrt(147) + sqrt(63).
Hence, the answer is d) sqrt(147) + sqrt(63).
To simplify the expression √21 (√7 + √3), we can first use the distributive property to expand it:
√21 (√7 + √3) = √21 √7 + √21 √3
Next, we simplify each part separately:
√21 √7 = √(21 × 7) = √147
√21 √3 = √(21 × 3) = √63
So, our expression becomes:
√147 + √63
But we can simplify this further. Let's find the perfect squares factors for both 147 and 63:
147 = 3 × 49 = 3 × 7²
63 = 3 × 21 = 3 × 7 × 3
Now we can rewrite our expression:
√147 + √63 = √(3 × 7²) + √(3 × 7 × 3)
Using the square root property, we can separate the factors:
= 7√3 + 3√3
= (7 + 3)√3
= 10√3
Therefore, the simplified expression is 10√3. None of the given answer choices match, so the correct answer is not listed.
√21√7 + √3
= √3√7√7 + √3
= 7√3+√3
= 8√3
the answer matching this is b)
but they should have simplified this.