Solve अम्नलिखित व्यंजकों में से प्रत्येक (5 + sqrt(5))(5 - sqrt(5)) NCE | 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

$$( 5 + \sqrt { 5 } ) ( 5 - \sqrt { 5 } )$$

Evaluate

$20$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

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

Calculate $5$ to the power of $2$ and get $25$.

$$25-\left(\sqrt{5}\right)^{2}$$

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

$$25-5$$

Subtract $5$ from $25$ to get $20$.

$$20$$

Factor

$2^{2}\times 5$