Question

Solve : 7√7 × (-4√2)
Simplyfy : √3/3 - √3/6
Simplyfy : 8√21 / 4√7
Solve : (1+√5) - (4+√5)
Solve : (3√2 - √8 + √32 - √2)​
Step By Step answer pls

Answer 1

Question 1 :

• $\tt\:7\sqrt{7} \times (-4\sqrt{2})$

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Solution :

$\tt\:7\sqrt{7} \times (-4\sqrt{2})$

Multiplying the numbers

$\tt\color{blue}{\implies\:-28 \sqrt{14}}$

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Question 2 :‎

• $\tt\:\frac{\sqrt{3}}{3} - \frac{\sqrt{3}}{6}$

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Solution :

$\tt\:\frac{\sqrt{3}}{3} - \frac{\sqrt{3}}{6}$

LCM of 3 and 6 = 6

$\tt\implies\:\frac{(2 \times \sqrt{3}) - (1 \times \sqrt{3}) }{6}$

Multiplying

$\tt\implies\:\frac{2\sqrt{3} - \sqrt{3}}{6}$

Performing subtraction in numerator

$\tt\implies\:\frac{1\sqrt{3}}{6}$

$\tt\color{blue}{\implies\:\frac{\sqrt{3}}{6}}$

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Question 3 :‎

• $\tt\:\frac{8\sqrt{21}}{4\sqrt{7}}$

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Solution :

$\tt\:\frac{8\sqrt{21}}{4\sqrt{7}}$

Reducing the fraction to lower terms

$\tt\implies\:\frac{\cancel{8}\sqrt{21}}{\cancel{4}\sqrt{7}}$

$\tt\implies\:\frac{2\sqrt{21}}{1\sqrt{7}}$

$\tt\color{blue}{\implies\:\frac{2\sqrt{21}}{\sqrt{7}}}$

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Question 4 :‎

• $\tt\:(1+\sqrt{5}) -(4+\sqrt{5})$

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Solution :

$\tt\:(1+\sqrt{5}) -(4+\sqrt{5})$

Multiplying the signs and removing our brackets

$\tt\implies\:1+\sqrt{5}-4-\sqrt{5}$

Arranging the numbers

$\tt\implies\:1-4+\sqrt{5}-\sqrt{5}$

Numbers with opposite signs gets cancelled out

$\tt\implies\:1-4+\cancel{\sqrt{5}}-\cancel{\sqrt{5}}$

$\tt\implies\:1-4$

$\tt\color{blue}{\implies\:(-3)}$

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Question 5 :‎

• $\tt\:3\sqrt{2}-\sqrt{8}+\sqrt{32}-\sqrt{2}$

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Solution :

$\tt\:3\sqrt{2}-\sqrt{8}+\sqrt{32}-\sqrt{2}$

Splitting the numbers under square root

$\tt\implies\:3\sqrt{2}-\sqrt{2 \times 2 \times 2}+\sqrt{2 \times 2 \times 2 \times 2 \times 2}-\sqrt{2}$

Now taking the numbers outside the square root

$\tt\implies\:3\sqrt{2}-2\sqrt{2}+2 \times 2\sqrt{2}-\sqrt{2}$

$\tt\implies\:3\sqrt{2}-2\sqrt{2}+4\sqrt{2}-\sqrt{2}$

Proceeding with simple calculation

$\tt\implies\:1\sqrt{2}+4\sqrt{2}-\sqrt{2}$

$\tt\implies\:\sqrt{2}+4\sqrt{2}-\sqrt{2}$

$\tt\implies\:5\sqrt{2}-\sqrt{2}$

$\tt\implies\:5\sqrt{2}-1\sqrt{2}$

$\tt\color{blue}{\implies\:4\sqrt{2}}$

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More to know :

Multiplication of surds -

• While multiplying the numbers with surds we first multiply the numbers outside the square root and then the numbers under square root.

Example :

2√5 × 4√3

First multiply 2 and 4 then √5 and √3

= 8√15

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Addition and subtraction of surds -

• The criteria for adding and subtracting surds is only that the numbers under the square root must be same.

Example :

(i) 5√7 + 10√7

As both the numbers have same numbers under square root i.e., 7 , we can easily add them

= 15√7

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(ii) 3√10 + 45√10

As both the numbers have same numbers under square root i.e., 10 , we can easily subtract them

= 48√7

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Note : Scroll left to right to view the answer properly. Hope it helps you :D~‎

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