multiply and simplify if possible.
sqrt(5x) (sqrt(x)-5 sqrt(5)
sqrt(5x)(sqrt(x))-5sqrt(5) = (sqrt(5))x - 5sqrt(5) = (sqrt(5))(x-5).
Why did the math book take a vacation to the beach? It needed some radical rest and a little square root beer! Now, let's get back to business and multiply and simplify:
sqrt(5x) (sqrt(x)-5 sqrt(5))
To multiply this, we can use the distributive property. So, let's break it down:
(sqrt(5x) * sqrt(x)) - (sqrt(5x) * 5 sqrt(5))
Now, let's multiply each term:
sqrt(5x * x) - 5 sqrt(5x * 5)
Simplifying further:
sqrt(5x^2) - 5 sqrt(25x)
Finally, simplify the square root of 5x^2 and square root of 25x:
x sqrt(5) - 5 * 5 sqrt(x)
Which simplifies to:
x sqrt(5) - 25 sqrt(x)
To multiply and simplify the expression:
Step 1: Distribute the square root into the parentheses.
√(5x) * (√x - 5√5)
Step 2: Simplify each term separately.
√(5x) * √x = √(5x * x) = √(5x²) = √5 * √x² = √5x
√(5x) * -5√5 = -5√(5x * 5) = -5√(25x) = -5√25 * √x = -5 * 5√x = -25√x
Step 3: Combine the simplified terms.
√(5x) * (√x - 5√5) = √5x - 25√x
So, the simplified expression is √5x - 25√x.
To multiply and simplify the expression sqrt(5x) (sqrt(x)-5 sqrt(5)), you can use the distributive property of multiplication over addition or subtraction. The distributive property states that for any real numbers a, b, and c, a * (b + c) = a * b + a * c.
So let's apply the distributive property to the given expression:
sqrt(5x) * sqrt(x) - sqrt(5x) * 5 * sqrt(5)
Now, simplifying each of the terms:
The first term, sqrt(5x) * sqrt(x), can be simplified by multiplying the square roots together to get sqrt(5x * x) or sqrt(5x^2).
The second term, sqrt(5x) * 5 * sqrt(5), can be simplified by multiplying the coefficients (numbers outside the square roots) together to get 5 * 5, resulting in 25, and multiplying the square roots together to get sqrt(5) * sqrt(5) = sqrt(5 * 5) = sqrt(25) = 5.
Putting it all together, the simplified expression becomes:
sqrt(5x^2) - 25 * sqrt(5)