Solve sqrt(2)(sqrt(14)+sqrt(5)) | 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

$$\sqrt{ 2 } ( \sqrt{ 14 } + \sqrt{ 5 } )$$

Evaluate

$\sqrt{10}+2\sqrt{7}\approx 8.453780282$

Solution Steps

Use the distributive property to multiply $\sqrt{2}$ by $\sqrt{14}+\sqrt{5}$.

$$\sqrt{2}\sqrt{14}+\sqrt{2}\sqrt{5}$$

Factor $14=2\times 7$. Rewrite the square root of the product $\sqrt{2\times 7}$ as the product of square roots $\sqrt{2}\sqrt{7}$.

$$\sqrt{2}\sqrt{2}\sqrt{7}+\sqrt{2}\sqrt{5}$$

Multiply $\sqrt{2}$ and $\sqrt{2}$ to get $2$.

$$2\sqrt{7}+\sqrt{2}\sqrt{5}$$

To multiply $\sqrt{2}$ and $\sqrt{5}$, multiply the numbers under the square root.

$$2\sqrt{7}+\sqrt{10}$$