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Question
2\sqrt{32}\times \left(\left(3\sqrt{24}\right)-\sqrt{10}\right)
Calculate the value
96\sqrt{3}-16\sqrt{5}
Alternative Form
\approx 130.49979
Evaluate
2\sqrt{32}\times \left(\left(3\sqrt{24}\right)-\sqrt{10}\right)
Simplify the root
More Steps
Evaluate
\sqrt{24}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{4\times 6}
\text{Write the number in exponential form with the base of }2
\sqrt{2^{2}\times 6}
The root of a product is equal to the product of the roots of each factor
\sqrt{2^{2}}\times \sqrt{6}
\text{Reduce the index of the radical and exponent with }2
2\sqrt{6}
2\sqrt{32}\times \left(\left(3\times 2\sqrt{6}\right)-\sqrt{10}\right)
Multiply the terms
2\sqrt{32}\times \left(6\sqrt{6}-\sqrt{10}\right)
Simplify the root
More Steps
Evaluate
\sqrt{32}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{16\times 2}
\text{Write the number in exponential form with the base of }4
\sqrt{4^{2}\times 2}
The root of a product is equal to the product of the roots of each factor
\sqrt{4^{2}}\times \sqrt{2}
\text{Reduce the index of the radical and exponent with }2
4\sqrt{2}
2\times 4\sqrt{2}\times \left(6\sqrt{6}-\sqrt{10}\right)
Multiply the terms
8\sqrt{2}\times \left(6\sqrt{6}-\sqrt{10}\right)
Multiply the terms
More Steps
Evaluate
8\left(6\sqrt{6}-\sqrt{10}\right)
Apply the distributive property
8\times 6\sqrt{6}-8\sqrt{10}
Multiply the terms
48\sqrt{6}-8\sqrt{10}
\left(48\sqrt{6}-8\sqrt{10}\right)\sqrt{2}
Apply the distributive property
48\sqrt{6}\times \sqrt{2}-8\sqrt{10}\times \sqrt{2}
Multiply the numbers
More Steps
Evaluate
48\sqrt{6}\times \sqrt{2}
Rewrite the expression
More Steps
Evaluate
\sqrt{6}\times \sqrt{2}
The product of roots with the same index is equal to the root of the product
\sqrt{6\times 2}
Calculate the product
\sqrt{12}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{4\times 3}
\text{Write the number in exponential form with the base of }2
\sqrt{2^{2}\times 3}
The root of a product is equal to the product of the roots of each factor
\sqrt{2^{2}}\times \sqrt{3}
\text{Reduce the index of the radical and exponent with }2
2\sqrt{3}
48\times 2\sqrt{3}
Multiply the terms
96\sqrt{3}
96\sqrt{3}-8\sqrt{10}\times \sqrt{2}
Solution
More Steps
Evaluate
-8\sqrt{10}\times \sqrt{2}
Rewrite the expression
More Steps
Evaluate
\sqrt{10}\times \sqrt{2}
The product of roots with the same index is equal to the root of the product
\sqrt{10\times 2}
Calculate the product
\sqrt{20}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{4\times 5}
\text{Write the number in exponential form with the base of }2
\sqrt{2^{2}\times 5}
The root of a product is equal to the product of the roots of each factor
\sqrt{2^{2}}\times \sqrt{5}
\text{Reduce the index of the radical and exponent with }2
2\sqrt{5}
-8\times 2\sqrt{5}
Multiply the terms
-16\sqrt{5}
96\sqrt{3}-16\sqrt{5}
Alternative Form
\approx 130.49979
Show Solutions
