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If $straight a open parentheses 2 space minus space square root of 3 close parentheses space equals space straight b space left parenthesis 2 space plus space square root of 3 right parenthesis space equals space 1 comma$ then the value of (a² - b²) is

$8 square root of 3$
$3 square root of 8$
$6 square root of 3$
$6 square root of 3$

55 Views

The simplified value of $6 square root of left parenthesis 27 right parenthesis to the power of negative 2 over 3 space end exponent plus space left parenthesis 8 right parenthesis to the power of negative 2 over 3 end exponent end root$ is

$6 square root of 35$
$fraction numerator 6 over denominator square root of 13 end fraction$
$square root of 13$
$square root of 13$

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4. $fraction numerator 1 over denominator square root of 1 plus square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 begin display style plus end style begin display style square root of 3 end style end fraction plus fraction numerator 1 over denominator square root of 3 begin display style plus end style begin display style square root of 4 end style end fraction plus.... plus fraction numerator 1 over denominator square root of 99 begin display style plus end style begin display style square root of 100 end style end fraction$ is equal to
$10 minus square root of 99$
$square root of 2 minus 10$
$7$
$7$

7

Shorcut Method:
Subtract the highest and lowest value
$square root of 100 space minus space square root of 1 space equals space 10 space minus space 1 space equals space 9$

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square root of 30 plus 12 square root of 6 end root space minus space square root of 4 plus 2 square root of 3 end root space minus space square root of 19 minus 6 square root of 2 end root

is simplified to

$3 square root of 2$
$square root of 2$
$2 square root of 3$
$2 square root of 3$

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open square brackets left parenthesis 0.0016 right parenthesis to the power of 0.16 end exponent space cross times space left parenthesis 0.0016 right parenthesis to the power of 0.09 end exponent close square brackets

is equal to

0.2
0.4
0.16
0.16

53 Views

fraction numerator 0.5 space cross times space 0.5 space cross times 0.5 space minus space 0.2 space cross times space 0.2 space cross times space 0.2 space plus space 0.3 space cross times space 0.3 space cross times space 0.3 space plus space 3 space cross times space 0.5 space cross times space 0.2 space cross times space 0.3 over denominator 0.5 space cross times space 0.5 space plus space 0.2 space cross times 0.2 space plus space 0.3 space cross times 0.3 space cross times space 0.3 space plus space 0.5 space cross times space 0.2 space plus space 0.2 space cross times space 0.3 space minus space 0.5 space cross times space 0.3 end fraction

is equal to

60 Views

The value of:
$fraction numerator 1 over denominator square root of left parenthesis 12 minus square root of 140 right parenthesis end root end root end fraction minus fraction numerator 1 over denominator square root of left parenthesis 8 minus square root of 60 right parenthesis end root end fraction minus fraction numerator 2 over denominator square root of left parenthesis 10 plus square root of 84 right parenthesis end root end fraction$