Multiply and simplify. Assume that no radicands were formed by raising negative numbers to even powers.
√6x3 √18x2
I have never been good at figuring this formula out with square roots and I am practicing for a test next week and I really want to graduate so if you can show me how to do the steps to this problem. Please and Thank you
You must know the first few perfect squares, such as
4, 9, 16, 25,... perhaps up to 144
so for √(any number) , attempt to split the number into factors containing one or more of those perfect squares.
e.g. √18 = √9 √2 = 3√2
√35 = √5√7 , nothing gained because neither 5 nor 7 is a perfect square.
If you have large numbers under the square root, such as
√1344
factor 1344 and hope to find a perfect square
e.g.
1344 = 4x336
= 4x4x84
= 4x4x4x21
= 64x21
So √1344 = √64√21 = 8√21
if you have √'s of variable powers, break them up into even exponent roots
remember √x^ = x
√x^4 = x^2
√x^6 = x^3 etc
e.g. √x^13
= √x^12 √x
= x^6 √x
Your last problem:
√18x2
= √9√2√x^2
= (3)(√2)(x)
= 3x√2
To multiply and simplify the given expression, √6x^3 * √18x^2, we need to apply the rules of multiplication and simplify the expression.
Step 1: Multiply the terms inside the square roots:
√6x^3 * √18x^2 = (√6 * √18) * (x^3 * x^2)
Step 2: Simplify the square root terms (√6 * √18):
To simplify, we can factorize the numbers inside the square root.
√6 can be written as √(2 * 3), and √18 can be written as √(2 * 3 * 3).
So, we can simplify √6 * √18 as √(2 * 3) * √(2 * 3 * 3).
Now, we can apply the rule that √a * √b = √(a * b):
√(2 * 3) * √(2 * 3 * 3) = √(2 * 3 * 2 * 3 * 3)
Step 3: Simplify the exponents (x^3 * x^2):
Using the rule of exponentiation, when multiplying variables with the same base, we add the exponents.
x^3 * x^2 = x^(3 + 2) = x^5
Putting all the simplified terms together:
√(2 * 3 * 2 * 3 * 3) * x^5
Step 4: Simplify the expression under the square root:
√(2 * 3 * 2 * 3 * 3) = √(2^2 * 3^3)
Using the rule that √(a^m * b^n) = a^(m/2) * b^(n/2):
√(2^2 * 3^3) = 2^(2/2) * 3^(3/2) = 2 * 3^(3/2)
Final answer:
The simplified expression is 2 * 3^(3/2) * x^5.
Remember, to simplify any expression, you need to apply the rules of arithmetic and algebra. Also, always double-check your answers by plugging in sample values and comparing them with the initial expression.