Help with factor large numbers

• Poker-face
In summary, the equation w + 14 = 1458 to the 4th root can be solved without factoring by adding -14 to both sides.

Poker-face

I am 31 and just started back in Math. My first class is Intermediate Algebra. I am sloving equations that force me to factor large numbers. Not sure if this is a skill that I was supposed to rember from high school, but nevertheless it is taking me a long time to do so. Can anyone tell me what the rules are when factor large roots. For example

1. w + 14 = 1458 to the 4th root.

EG

Poker-face said:
I am 31 and just started back in Math. My first class is Intermediate Algebra. I am sloving equations that force me to factor large numbers. Not sure if this is a skill that I was supposed to rember from high school, but nevertheless it is taking me a long time to do so. Can anyone tell me what the rules are when factor large roots. For example

1. w + 14 = 1458 to the 4th root.

EG
I'm not sure what your equation is. Is it this?
$$w + 14 = \sqrt[4]{1458}$$

Click on the equation I wrote to see the LaTeX script I wrote for this equation.

If that's the equation you want to solve, there is no factoring needed. All you have to do to solve for w is to add -14 to both sides of the equation.

Mark44 said:
I'm not sure what your equation is. Is it this?
$$w + 14 = \sqrt[4]{1458}$$

Click on the equation I wrote to see the LaTeX script I wrote for this equation.

If that's the equation you want to solve, there is no factoring needed. All you have to do to solve for w is to add -14 to both sides of the equation.

Yes. How do you simplfy the square root?

Poker-face said:
Yes. How do you simplfy the square root?
That's a fourth root.
Simplify it by finding all factors and seeing if any are to the fourth or higher power. For this problem, 1458 = 2 * 729 = 2 * 9 * 81 = 2 * 93 = 2 * 36

The last expression can also be written as 34 * 2 * 9 = 34 * 18

Now use the property of square roots, cube roots, fourth roots, etc. that says
$$\sqrt[n]{ab} = \sqrt[n]{a}\sqrt[n]{b}$$

For even roots (square root, fourth root, etc.) in the equation above, both a and b have to be nonnegative. For odd roots (cube root, fifth root, etc.) a and be can be any real numbers.

I understand the rule but how you get to step two - 2 x 9 x 81

729 = 9 * 81. I used the concept I mentioned to you in another thread - if the sum of the digits of a number is 9 or a multiple of 9, the number is divisible by 9.

So 1458 = 2 * 729 = 2 * 9 * 81

Mark44 said:
729 = 9 * 81. I used the concept I mentioned to you in another thread - if the sum of the digits of a number is 9 or a multiple of 9, the number is divisible by 9.

So 1458 = 2 * 729 = 2 * 9 * 81

Thanks again both threads were a big help!

EG

What is the purpose of factoring large numbers?

The purpose of factoring large numbers is to break down a large number into smaller factors that are more manageable and easier to work with.

What is the best method for factoring large numbers?

The most commonly used method for factoring large numbers is the trial and error method, where you test different potential factors until you find the correct ones.

What are the common techniques used for factoring large numbers?

Some common techniques used for factoring large numbers include using prime factorization, the difference of squares method, and the quadratic formula.

How do you check if a factor is correct for a large number?

To check if a factor is correct for a large number, you can multiply the factor by the other factors to see if it equals the original number. You can also use a calculator to confirm the factor.

Why is factoring large numbers important in science?

Factoring large numbers is important in science because it allows for more accurate and efficient calculations, especially in fields like cryptography and number theory. It also helps in understanding the properties and relationships between numbers, which is essential in many scientific studies.