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likoan [24]
3 years ago
8

%20%5Cfrac%7B%20%5Csqrt%7B7%20-%20%20%5Csqrt%7B24%7D%20%7D%20%7D%7B2%7D%20" id="TexFormula1" title=" \frac{ \sqrt{7 + \sqrt{24} } } 2{ + } \frac{ \sqrt{7 - \sqrt{24} } }{2} " alt=" \frac{ \sqrt{7 + \sqrt{24} } } 2{ + } \frac{ \sqrt{7 - \sqrt{24} } }{2} " align="absmiddle" class="latex-formula">
​

Mathematics
1 answer:
lozanna [386]3 years ago
6 0

Answer:

√6

Step-by-step explanation:

We have to find the value of the expression \frac{\sqrt{7+\sqrt{24} } }{2} +\frac{\sqrt{7-\sqrt{24} } }{2}.

Let, A = \frac{\sqrt{7+\sqrt{24} } }{2} +\frac{\sqrt{7-\sqrt{24} } }{2}

⇒ A^{2} = \frac{7+\sqrt{24} }{4} +\frac{7-\sqrt{24} }{4}+ 2\times \frac{\sqrt{7+\sqrt{24} } }{2} \times \frac{\sqrt{7-\sqrt{24} } }{2} {Squaring both sides. Since (a + b)² = a² + b² + 2ab}

⇒ A^{2} = \frac{7+\sqrt{24}+7-\sqrt{24}  }{4} + 2 \times \frac{\sqrt{49-24} }{4} {Since (a + b)(a - b) = a² - b²}

⇒ A^{2}= \frac{7}{2}  +2 \times \frac{5}{4}

⇒ A^{2} = \frac{7}{2} +\frac{5}{2} = 6

⇒ A = √6 (Answer) {Neglecting the negative root as the original expression is positive}

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Determine the solution set of x2 - 80 = 0
meriva

                                         x²  -  80  =  0
Add 80
to each side:                      x²          =  80

Square root
each side:                         x            =  √80

Look it up:                        x  =  + 8.944... (rounded)
                                 and
                                       x  =  - 8.944...  (rounded).
___________________________________

Here's a cleaner solution:

                                         x²  -  80  =  0
Add 80
to each side:                      x²          =  80

Square root
each side:                         x            =  √80

 But  80 = 16 · 5

 So     √80  =  √16 · √5

            √16 = 4, so            x  = 4 √5      

 

8 0
3 years ago
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butalik [34]

Answer:

Step-by-step explanation:

The drawing of the garage is a smaller representation of the actual garage. A garage is drawn using a scale of 2 2/3 inch = 6feet. Let us first convert 2 2/3 inch to improper fraction. It becomes 8/3 inch.

Let us determine the unit measurement.

If 6feet = 8/3 inch,

1 foot will be 8/3 ÷ 6 = 8/3×1/6

= 8/18 inches. Therefore

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68 × 8/18 = 272/9 = 30 2/9 inches

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X = 8

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Luda [366]
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6 0
3 years ago
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Andrej [43]

Answer:

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