(A) Given the expression: $(\sqrt{5}+3)^{2} = a+b\sqrt{5}$.Using the algebraic identity $(x+y)^{2} = x^{2} + 2xy + y^{2}$,where $x = \sqrt{5}$ and $y

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) Given the expression: $(\sqrt{5}+3)^{2} = a+b\sqrt{5}$.Using the algebraic identity $(x+y)^{2} = x^{2} + 2xy + y^{2}$,where $x = \sqrt{5}$ and $y = 3$:$(\sqrt{5})^{2} + 2(\sqrt{5})(3) + (3)^{2} = a+b\sqrt{5}$.$5 + 6\sqrt{5} + 9 = a+b\sqrt{5}$.$14 + 6\sqrt{5} = a+b\sqrt{5}$.By comparing the rational and irrational parts on both sides,we get $a = 14$ and $b = 6$.

Class 9 Mathematics Number Systems Mix Examples - Number Systems

Medium

For each question,select the proper option from four options given,to make the statement true: If $(\sqrt{5}+3)^{2}=a+b \sqrt{5}$,then........

A
$a=14, b=6$
B
$a=8, b=3$
C
$a=14, b=3$
D
$a=8, b=6$

Explore More

Browse All

Question Bank

All Subjects

Class 9 Questions

Class 9

Mathematics Questions

Chapter

Number Systems

Subtopic

Mix Examples - Number Systems

Fill in the blanks to make the following statement true: The decimal expansion of $\frac{2}{3}$ is of $\ldots \ldots$ type.

Easy

View Solution

For each question,select the proper option from four options given,to make the statement true: The decimal expansion of $-\frac{11}{4}$ is..........

Easy

View Solution

State the number which is a whole number but not a natural number.

Easy

View Solution

Insert a rational number and an irrational number between $2$ and $3$.

Easy

View Solution

If $x = 2 + \sqrt{3},$ then find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{3} + \frac{1}{x^{3}}.$

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

For each question,select the proper option from four options given,to make the statement true: If $(\sqrt{5}+3)^{2}=a+b \sqrt{5}$,then........

Similar Questions

Fill in the blanks to make the following statement true: The decimal expansion of $\frac{2}{3}$ is of $\ldots \ldots$ type.

For each question,select the proper option from four options given,to make the statement true: The decimal expansion of $-\frac{11}{4}$ is..........

State the number which is a whole number but not a natural number.

Insert a rational number and an irrational number between $2$ and $3$.

If $x = 2 + \sqrt{3},$ then find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{3} + \frac{1}{x^{3}}.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module