Question

sqrt 98n^19

Answer 1

\( \large \sqrt{98n^{19} } \)

What is the largest perfect square factor of 98?
What is the largest perfect square factor of \(n^{19}\) ?

Answer 2

n^19 is n^9 sqrt n

Answer 3

Correct.
The largest perfect square factor on \( n^{19}\) is \(n^{18} \) since 18 is an even exponent, so
\(\sqrt {n^{19}} = \sqrt{n^{18} n} = n^9 \sqrt{n} \)

Now can you find the prime factors of 98?

Answer 4

um im not sure this always confuses me ): @mathstudent55

Answer 5

Do the prime factorization of 98... you can stop here, since 49 is 7^2
\[\Large \sqrt{98n^{19} } = n^9 \sqrt{98n}\]so change 98 into 2*49, then break up the square root.

\[\Large n^9 \sqrt{49*2 n} = n^9 \sqrt{49} \sqrt{2 n}\]

Answer 6

I'll show you how to factor a number into its prime factors.

Answer 7

One method is to divide the number by the prime numbers repeatedly.
First, familiarize yourself with the first several prime numbers.
Here are the first 10 prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Answer 8

To find the prime factors of any number, you try to divide the number by the prime numbers in order, starting with 2. Divide the number by 2 as many times as possible. When it is no longer divisible by 2, move on to 3. Keep on going until the result of your division is 1. Then you wil have all prime factors listed.

Answer 9

so is the simplified expression n^9 sqrt 49 sqrt 2n + n^9 sqrt n ? im a little confused

Answer 10

Well the square root of 49 is 7, and remember that everything is multiplied together (there's no addition) so if you understand up to here, you can simplify this\[\Large n^9 \sqrt{49} \sqrt{2 n}\]

Answer 11

Let's do it for 98, the number in this problem.
Is 98 divisible by 2? Yes, so
98/2 = 49
49 is not divisible by 2, 3, or 5, so we move on to 7.
49/7 = 7
7/7 = 1

The prime factors of 98 are 2, 7, 7
That means \(98 = 2 \times 7^2\)

Answer 12

Now that you know that
\(98 = 2 \times 7^2\), you can rewrite your root as:
\(\sqrt{98} = \sqrt{2 \times 7^2} = \sqrt{2}\sqrt{7^2} = 7\sqrt{2} \)

Answer 13

Maybe break it up like this: \[\Large \sqrt{98n^{19} } = \sqrt{98} * \sqrt{n^{19}}\]

Answer 14

The answer, then is:
\( \sqrt{98n^{19}} \)
\(= 7n^9\sqrt{2n} \)

Answer 15

Still confused @sylinan ?

Answer 16

\[\Large \sqrt{98n^{19} } = \sqrt{98} * \sqrt{n^{19}} \]
\[\Large \sqrt{49*2} * n^9 \sqrt n\]
\[\Large \sqrt{49} *\sqrt{2} * n^9 \sqrt n\]follow?

Answer 17

sorry my computer froze @mathstudent55 and @agent0smith but i kind of get it

Answer 18

great

Answer 19

thank you (:

Answer 20

wlcm