Simplify each radical expression. Leave in radical form. Show your work.
6.sqrt 75 + sqrt 3
7. sqrt7(sqrt 14 + sqrt3 )
please.
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Is this correct
To simplify radical expressions, we need to look for perfect square factors inside the square root. Let's start with each problem:
6. √75 + √3
First, let's find the perfect square factors of 75:
75 = 25 * 3
Now, we can rewrite the expression using perfect square factors:
√(25 * 3) + √3
Next, we can simplify the square root of 25:
√25 = 5
Applying this, our expression becomes:
5√3 + √3
Since both terms have the same radical term (√3), we can combine them, resulting in:
(5 + 1)√3 = 6√3
Thus, the simplified expression is 6√3.
Now, let's move on to the next problem:
7. √7(√14 + √3)
First, let's simplify the square root terms inside the parentheses:
√14 cannot be simplified further since it doesn't have any perfect square factors.
√3 also cannot be simplified further.
Now, we can rewrite the expression with the simplified square roots:
√7(√14 + √3)
Since there are no perfect square factors to combine, the expression remains the same.
Therefore, the simplified expression is √7(√14 + √3).
6. √75 + √3
= √25√3 + √3
= 5√3 + √3
= 6√3
7.
√7(√14 + √3)
= √98 + √21
= √49√2 + √21
= 7√2 + √21