Express in simplest radical form.
2√72 + 8√98
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.
To simplify the given expression, we need to simplify each term individually and then add them together.
1. Simplify √72:
We can find the factors of 72:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
The largest perfect square factor is 36 (6^2), so we can write:
√72 = √(36 * 2)
Using the property √(a * b) = √a * √b:
√(36 * 2) = √36 * √2
√72 = 6√2
2. Simplify √98:
We can find the factors of 98:
1, 2, 7, 14, 49, 98.
The largest perfect square factor is 49 (7^2), so we can write:
√98 = √(49 * 2)
Using the property √(a * b) = √a * √b:
√(49 * 2) = √49 * √2
√98 = 7√2
Now, we can substitute the simplified values back into the expression:
2√72 + 8√98 = 2(6√2) + 8(7√2)
Simplifying further:
2(6√2) + 8(7√2) = 12√2 + 56√2
Combining like terms:
12√2 + 56√2 = (12 + 56)√2
12√2 + 56√2 = 68√2
Therefore, the expression 2√72 + 8√98 simplifies to 68√2 in its simplest radical form.
To express the expression 2√72 + 8√98 in simplest radical form, we need to simplify the square roots and then combine like terms.
First, let's simplify each square root individually:
√72 can be simplified by finding the largest perfect square that is a factor of 72. The largest perfect square that divides 72 is 36, which is equal to 6². So we can write √72 as √(6² * 2).
Using the property of square roots, we can separate the square root into two separate square roots:
√(6² * 2) = √6² * √2 = 6√2.
Next, let's simplify √98. Following a similar process, we can rewrite it as √(7² * 2):
√(7² * 2) = √7² * √2 = 7√2.
Now, we can substitute the simplified square roots back into the original expression:
2√72 + 8√98 = 2(6√2) + 8(7√2).
Multiplying the coefficients and keeping the same radicals:
= 12√2 + 56√2.
Finally, we can combine the like terms:
12√2 + 56√2 = (12 + 56)√2 = 68√2.
Therefore, the expression 2√72 + 8√98 simplified in simplest radical form is 68√2.