Question

simplify (7+4√3) (7-4 root 3)​

Answer 1

Answer:

1

Step-by-step explanation:

49-28√3+28√3-48

=1

hope it helps you........

Answer 2

Answer:

Required answer is 1

Step-by-step explanation:

Given, (7+4√3) (7-4√ 3)

We want to simplify the given term.

Now,

We know,

${x}^{2} - {y}^{2} \\ = (x + y)(x - y)$

Now,

$x = 7 \\ y = 4 \sqrt{3}$

So,

$(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3} ) \\ = {7}^{2} - {(4 \sqrt{3} )}^{2} \\ = 49 - 16 \times 3 \\ = 49 - 48 \\ = 1$

Here applied formula,

$\sqrt{x} \times \sqrt{x} = {( \sqrt{x}) }^{2} = x$

This a problem of Power of indices .

Some important formulas of Power of indices.

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Power of indices related two more questions:

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