Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Calculate the product and express in reduced form.\newline45×5\sqrt{45}\times\sqrt{5}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Multiply radical expressionsright chevron icon

Full solution

Q. Calculate the product and express in reduced form.\newline45×5\sqrt{45}\times\sqrt{5}
  1. Find Prime Factorization: Find the prime factorization of 45\sqrt{45} and 5\sqrt{5}. The prime factorization of 4545 is 3×3×53 \times 3 \times 5, and the prime factorization of 55 is just 55. So, 45×5\sqrt{45} \times \sqrt{5} can be expressed as 3×3×5×5\sqrt{3 \times 3 \times 5} \times \sqrt{5}.
  2. Combine Square Roots: Apply the multiplication property of square roots to combine them. So, 3×3×5×5=3×3×5×5\sqrt{3 \times 3 \times 5} \times \sqrt{5} = \sqrt{3 \times 3 \times 5 \times 5}.
  3. Group Perfect Squares: Group the perfect square factors in 3×3×5×5\sqrt{3 \times 3 \times 5 \times 5}. So, 3×3×5×5=32×52\sqrt{3 \times 3 \times 5 \times 5} = \sqrt{3^2 \times 5^2}.
  4. Pull Out Base: Pull out the base of perfect square factors from 32×52\sqrt{3^2 \times 5^2}. So, 32×52=3×5\sqrt{3^2 \times 5^2} = 3 \times 5.
  5. Simplify Result: Simplify 3×53 \times 5. So, 45×5=3×5=15\sqrt{45} \times \sqrt{5} = 3 \times 5 = 15.

More problems from Multiply radical expressions

Question
Order the expressions from least to greatest.\newline11182−6022×5 11^{1} \quad8^{2}-60 \quad 2^{2} \times 5
Get tutor helpright-arrow

Posted 4 months ago

Question
Order the expressions from least to greatest.\newline23−2121+3132 2^{3}-2^{1} \quad 2^{1}+3^{1} \quad 3^{2}
Get tutor helpright-arrow

Posted 4 months ago

Question
Let y=ex y=\sqrt{e^{x}} .\newlineFind dydx \frac{d y}{d x} .\newlineChoose 11 answer:\newline(A) ex2 \frac{\sqrt{e^{x}}}{2} \newline(B) ex \sqrt{e^{x}} \newline(C) xex−1 x \sqrt{e^{x-1}} \newline(D) 12ex \frac{1}{2 \sqrt{e^{x}}}
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the area of the region between the graphs of f(x)=−x2+2x+12 f(x)=-x^{2}+2 x+12 and g(x)=x2−12 g(x)=x^{2}-12 from x=−3 x=-3 to x=4 x=4 ?\newlineChoose 11 answer:\newline(A) 77\newline(B) 3433 \frac{343}{3} \newline(C) 833 \frac{83}{3} \newline(D) 52313−1−323 \frac{52}{3} \sqrt{13}-1-32 \sqrt{3}
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the average value of 1x \frac{1}{x} on the interval 4≤x≤8 4 \leq x \leq 8 ?\newlineChoose 11 answer:\newline(A) 316 \frac{3}{16} \newline(B) 116 \frac{1}{16} \newline(C) ln⁡(32)4 \frac{\ln (32)}{4} \newline(D) ln⁡(2)4 \frac{\ln (2)}{4}
Get tutor helpright-arrow

Posted 3 months ago

Question
Part 44 of 66\newlineKK\newlineFor the data given below, answer parts (a) through (f).\newline\begin{array}{cc}\newlinex & y (\newline\)−19-19 & 102102 (\newline\)−16-16 & 122122 (\newline\)−14-14 & 120120 (\newline\)−13-13 & 132132 (\newline\)−9-9 & 142142 (\newline\)\end{array}\newline(a) Draw a scatter plot.\newlineChoose the correct graph below.\newlineA.\newlineB.\newlineC.\newlineD.\newline(b) Find the equation of the line containing the first and the last data points.\newliney=4x+178y=4x+178\newline(Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)\newline(c) Graph the line found in part (b) on the scatter plot.\newlineChoose the correct graph below.\newlineA.\newlineB\newlineC.\newline(d) Use a graphing utility to find the line of best fit.\newliney=□x+□y=\square x+\square\newline(Type integers or decimals rounded to four decimal places as needed)
Get tutor helpright-arrow

Posted 3 months ago

Question
noot: Additional Practice (LMS graded)\newlineof 22\newlinee surface area of a paper cup is defined by the function \newlines(h)=6π16+h2s(h)=6\pi\sqrt{16+h^{2}}, where \newlinehh is the height of the cup. What is the domain and range of \newlines(h)s(h) ?\newlineDescribe the domain. Select the correct choice below and, if necessary, fill in the answer box within your choice.\newlineA. The domain is \newline{h∣h>−}\{h\mid h>-\}.\newline(Type an inequality or a compound inequality. Simplify your answer. Type an exact answer, using \newlineπ\pi as needed.)\newlineB. The domain is all real numbers.
Get tutor helpright-arrow

Posted 3 months ago

Question
Determine the coefficient and degree of the monomial.\newline−7x2y5-7x^{2}y^{5}\newlineThe coefficient of the monomial is \newline□\square.\newlineThe degree of the monomial is \newline□\square.
Get tutor helpright-arrow

Posted 3 months ago

Question
a2a−5a−3a0⋅(a2a3)−4=ax\dfrac{a^2a^{-5}}{a^{-3}a^0}\cdot\left(\dfrac{a^2}{a^3}\right)^{-4}=a^x
Get tutor helpright-arrow

Posted 3 months ago

Question
x3+4x5=13\frac{x}{3} + \frac{4x}{5} = \frac{1}{3}
Get tutor helpright-arrow

Posted 3 months ago

View all (18)