Simplify 9 root 72
2 root 24. (This question contains a numerator and a denominator.)
The answer is 9 root 3 divided by 2 but I can't figure out how to get the answer.
9√72 / 2√24
= 9√(3*24) / 2√24
= 9√3√24 / 2√24
= 9√3/2
To simplify the given expression, we need to simplify the radicals in both the numerator and the denominator separately, and then divide the results.
Let's first simplify the numerator, which is 9√72. To simplify the radical, we need to find the largest perfect square that divides evenly into 72. In this case, 36 is the largest perfect square that divides 72. So we can rewrite 72 as 36 × 2.
Now, let's substitute that back into the expression: 9√(36 × 2). Using the property of radicals, we can split it into two separate radicals: 9√36 × √2.
The square root of 36 is 6, so we have: 9 × 6 × √2 = 54√2.
Now let's simplify the denominator, which is 2√24. Again, we need to find the largest perfect square that divides evenly into 24. In this case, it is 4. So we rewrite 24 as 4 × 6.
Substituting back into the expression: 2√(4 × 6). Using the property of radicals, we split it into two separate radicals: 2√4 × √6.
The square root of 4 is 2, so we have: 2 × 2 × √6 = 4√6.
Finally, we divide the numerator (54√2) by the denominator (4√6): 54√2 / 4√6. To divide by a radical, we multiply the numerator and the denominator by the conjugate of the denominator (√6 - multiplying both the numerator and the denominator by √6).
(54√2 * √6) / (4√6 * √6) = (54√12) / (4 * 6) = (54√12) / 24.
Now, simplify the radical: √12 = 2√3.
Finally, we have: (54 * 2√3) / 24 = 108√3 / 24.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 12.
(108/12) * (√3 / 24) = 9√3 / 2.
So, the simplified expression is 9√3 / 2.