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Find the positive root of 3x2+6−−−−−−√=9

Find the positive root of 3x2+6−−−−−−√=9

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
12 days ago
The square root of the number “n” is the number when multiplied by itself and equals to “n”. For example square root of 9–√=32−−√=3 Complete step by step solution: Given that 3x2+6−−−−−−√=9 Squaring on both the sides of the equation – (3x2+6−−−−−−√)2=92 As per the property – the square and the square root cancels each other. 3x2+6=81 Take all constants on the right hand side of the equation. 3x2=81−6 Signofthenumberchangeswhenwechangetheside,positivechangestonegativeandnegativechangestopositivesign 3x2=75 x2=753 Whennumberfrommultiplicationchangesside,itgoestothedenominatorfromthenumerator x2=25 Take square root on both the sides – x2−−√=25−−√ As we know that – the square and the square root cancels each other. x=±5x=5 or x=(−5) Here, x=(−5) is not applicable. As here, we are asked to find the positive square root, therefore x=5 is the required answer. Hence, the positive root of 3x2+6−−−−−−√=9 is x=5 Note: The squares and the square roots are opposite to each other and so cancel each other. Perfect square number is the square of an integer, simply it is the product of the same integer with itself. For example - 25 = 5 × 5, 25 = 52, generally it is denoted by n to the power two i.e. n2. The perfect square is the number which can be expressed as the product of the two equal integers. For example: 9, it can be expressed as the product of equal integers. 9=3×3

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