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:

Express in simplest radical form. (sqrt560)/(sqrt7) Answer:

Express in simplest radical form.\newline5607 \frac{\sqrt{560}}{\sqrt{7}} \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Simplify radical expressions with root inside the rootright chevron icon

Full solution

Q. Express in simplest radical form.\newline5607 \frac{\sqrt{560}}{\sqrt{7}} \newlineAnswer:
  1. Factor and Simplify: Simplify the square root of 560560.\newlineTo simplify the square root of 560560, we need to factor 560560 into its prime factors and look for pairs of the same number, since the square root of a pair of numbers is just that number.\newline560=2×280560 = 2 \times 280\newline560=2×2×140560 = 2 \times 2 \times 140\newline560=2×2×2×70560 = 2 \times 2 \times 2 \times 70\newline560=2×2×2×2×35560 = 2 \times 2 \times 2 \times 2 \times 35\newline560=2×2×2×2×5×7560 = 2 \times 2 \times 2 \times 2 \times 5 \times 7\newlineNow we can pair the 22s and take them out of the square root.\newline560=2×2×2×2×5×7\sqrt{560} = \sqrt{2 \times 2 \times 2 \times 2 \times 5 \times 7}\newline560=2×2×5×7\sqrt{560} = 2 \times 2 \times \sqrt{5 \times 7}\newline560=4×35\sqrt{560} = 4 \times \sqrt{35}
  2. Simplify Square Root of 77: Simplify the square root of 77. The square root of 77 cannot be simplified further since 77 is a prime number. 7=7\sqrt{7} = \sqrt{7}
  3. Divide Simplified Square Roots: Divide the simplified square root of 560560 by the square root of 77. Now we divide 4×354 \times \sqrt{35} by 7\sqrt{7}. (4×35)/(7)(4 \times \sqrt{35}) / (\sqrt{7}) We can simplify this by dividing the square root of 3535 by the square root of 77. (4×35)/(7)=4×(35/7)(4 \times \sqrt{35}) / (\sqrt{7}) = 4 \times (\sqrt{35} / \sqrt{7})
  4. Simplify Division of Square Roots: Simplify the division of the square roots.\newlineWe can simplify 35/7\sqrt{35} / \sqrt{7} by recognizing that 35\sqrt{35} is the same as 5×7\sqrt{5 \times 7} and we can divide by 7\sqrt{7}.\newline35/7=5×7/7\sqrt{35} / \sqrt{7} = \sqrt{5 \times 7} / \sqrt{7}\newline35/7=5\sqrt{35} / \sqrt{7} = \sqrt{5}
  5. Multiply by 44: Multiply the result by 44.\newlineNow we multiply the simplified square root by 44.\newline4×54 \times \sqrt{5}\newlineThis is the simplest radical form of the original expression.

More problems from Simplify radical expressions with root inside the root

Question
Find the real-number root. \newline16\sqrt{16}\newline\newlineWrite your answer in simplified form. \newline____\_\_\_\_
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the real-number root. \newline916\sqrt{\frac{9}{16}}\newlineSimplify your answer and write it as a decimal or as a proper or improper fraction.\newline_____\_\_\_\_\_
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the real-number root using a calculator. Round your answer to the nearest thousandth. \newline`\sqrt{957} `\newline _______
Get tutor helpright-arrow

Posted 9 months ago

Question
Multiply. Write your answer in simplest form. \newline273×42\sqrt{273} \times \sqrt{42}\newline______
Get tutor helpright-arrow

Posted 7 months ago

Question
Simplify. \newline634\sqrt{\frac{63}{4}}\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify. Rationalize the denominator.\newline−49−2\frac{-4}{9 - \sqrt{2}}\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve for z z .\newline16=z 16 = \sqrt{z} \newlinez= z = _____
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify the radical expression. 14x14 \sqrt{14x^{14}} Write your answer in the form A A , B \sqrt{B} , or AB A\sqrt{B} , where A A and B B are constants or expressions in x x . Use at most one radical in your answer, and at most one absolute value symbol in your expression for A A . ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify the radical expression.\newline12x12\sqrt{12x^{12}}\newlineWrite your answer in the form AA, B\sqrt{B}, or ABA\sqrt{B}, where AA and BB are constants or expressions in xx. Use at most one radical in your answer, and at most one absolute value symbol in your expression for AA.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 9 months ago

Question
What is the value of sin⁡(5π6)? \sin \left(\frac{5 \pi}{6}\right) ? \newlineChoose 11 answer:\newline(A) −32 -\frac{\sqrt{3}}{2} \newline(B) −22 -\frac{\sqrt{2}}{2} \newline(C) 12 \frac{1}{2} \newline(D) 150150
Get tutor helpright-arrow

Posted 10 months ago

View all (51)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant