To express the given expression in simplest radical form, we need to simplify the radicals.
First, let's simplify the radical of 72. We can factor 72 to find its perfect square factors:
72 = 2 * 2 * 2 * 3 * 3
There is at least one pair of each factor, so we can take them out of the radical:
√72 = √(2 * 2 * 2 * 3 * 3)
= 2 * 3 * √2
= 6√2
Now, let's simplify the radical of 98. We can factor 98 to find its perfect square factors:
98 = 2 * 7 * 7
There is one pair of 7, so we can take them out of the radical:
√98 = √(2 * 7 * 7)
= 7√2
Substituting the simplified radicals back into the expression:
2√72 + 8√98 = 2(6√2) + 8(7√2)
Simplifying further:
= 12√2 + 56√2
Combining like terms:
= (12 + 56)√2
= 68√2
Therefore, the given expression in simplest radical form is 68√2.
Express in simplest radical form.
2√72 + 8√98
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