Solve (sqrt(2 + 1))/(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

$$\frac{\sqrt{2+1}}{\sqrt{5}}$$

Evaluate

$\frac{\sqrt{15}}{5}\approx 0.774596669$

Solution Steps

Add $2$ and $1$ to get $3$.

$$\frac{\sqrt{3}}{\sqrt{5}}$$

Rationalize the denominator of $\frac{\sqrt{3}}{\sqrt{5}}$ by multiplying numerator and denominator by $\sqrt{5}$.

$$\frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of $\sqrt{5}$ is $5$.

$$\frac{\sqrt{3}\sqrt{5}}{5}$$

To multiply $\sqrt{3}$ and $\sqrt{5}$, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{5}$$