Solve (11sqrt(12)-13sqrt(8))(14sqrt(12)-sqrt(8) | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(11 \sqrt{ 12 } -13 \sqrt{ 8 } )(14 \sqrt{ 12 } - \sqrt{ 8 }$$

Evaluate

$1952-772\sqrt{6}\approx 60.993918571$

Solution Steps

Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.

$$\left(11\times 2\sqrt{3}-13\sqrt{8}\right)\left(14\sqrt{12}-\sqrt{8}\right)$$

Multiply $11$ and $2$ to get $22$.

$$\left(22\sqrt{3}-13\sqrt{8}\right)\left(14\sqrt{12}-\sqrt{8}\right)$$

Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.

$$\left(22\sqrt{3}-13\times 2\sqrt{2}\right)\left(14\sqrt{12}-\sqrt{8}\right)$$

Multiply $-13$ and $2$ to get $-26$.

$$\left(22\sqrt{3}-26\sqrt{2}\right)\left(14\sqrt{12}-\sqrt{8}\right)$$

Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.

$$\left(22\sqrt{3}-26\sqrt{2}\right)\left(14\times 2\sqrt{3}-\sqrt{8}\right)$$

Multiply $14$ and $2$ to get $28$.

$$\left(22\sqrt{3}-26\sqrt{2}\right)\left(28\sqrt{3}-\sqrt{8}\right)$$

Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.

$$\left(22\sqrt{3}-26\sqrt{2}\right)\left(28\sqrt{3}-2\sqrt{2}\right)$$

Apply the distributive property by multiplying each term of $22\sqrt{3}-26\sqrt{2}$ by each term of $28\sqrt{3}-2\sqrt{2}$.

$$616\left(\sqrt{3}\right)^{2}-44\sqrt{3}\sqrt{2}-728\sqrt{3}\sqrt{2}+52\left(\sqrt{2}\right)^{2}$$

The square of $\sqrt{3}$ is $3$.

$$616\times 3-44\sqrt{3}\sqrt{2}-728\sqrt{3}\sqrt{2}+52\left(\sqrt{2}\right)^{2}$$

Multiply $616$ and $3$ to get $1848$.

$$1848-44\sqrt{3}\sqrt{2}-728\sqrt{3}\sqrt{2}+52\left(\sqrt{2}\right)^{2}$$

To multiply $\sqrt{3}$ and $\sqrt{2}$, multiply the numbers under the square root.

$$1848-44\sqrt{6}-728\sqrt{3}\sqrt{2}+52\left(\sqrt{2}\right)^{2}$$

To multiply $\sqrt{3}$ and $\sqrt{2}$, multiply the numbers under the square root.

$$1848-44\sqrt{6}-728\sqrt{6}+52\left(\sqrt{2}\right)^{2}$$

Combine $-44\sqrt{6}$ and $-728\sqrt{6}$ to get $-772\sqrt{6}$.

$$1848-772\sqrt{6}+52\left(\sqrt{2}\right)^{2}$$

The square of $\sqrt{2}$ is $2$.

$$1848-772\sqrt{6}+52\times 2$$

Multiply $52$ and $2$ to get $104$.

$$1848-772\sqrt{6}+104$$

Add $1848$ and $104$ to get $1952$.

$$1952-772\sqrt{6}$$