Question

1) (√18+√2)*22) (√11+3)²-6√113) (2+√3)²+(2-√3)²4) (√21*√14)/√6

Answer 1

Ответ:

$1)( \sqrt{18 } + \sqrt{2} ) \times 2 = (3 \sqrt{2} + \sqrt{2} ) \times 2 = 4 \sqrt{2} \times 2 = 8 \sqrt{2}$

$2) (\sqrt{11} + 3) {}^{2} - 6 \sqrt{11} = 11 + 6 \sqrt{11} + 9 - 6 \sqrt{11} = 20$

$3)(2x + \sqrt{3} ) {}^{2} + (2 - \sqrt{3} ) {}^{2} = 4x {}^{2} + 4 \sqrt{3} x + 3 + 4 - 4 \sqrt{3} + 3 = 4x {}^{2} + 4 \sqrt{3} x + 10 - 4 \sqrt{3}$

$4)( \sqrt{21 } \times \sqrt{14} )\div \sqrt{6} = \sqrt{294} \div \sqrt{6} = (7 \sqrt{6} ) \div \sqrt{6} = 7$

Answer 2

To calculate the given expression, let's break it down step by step:

Step 1: Calculate (√18 + √2) To simplify this, we can evaluate the square roots separately: √18 = √(9 * 2) = 3√2 √2 remains unchanged. So, (√18 + √2) = (3√2 + √2) = 4√2

Step 2: Multiply (4√2 * 22) To multiply a number by a square root, we can simply multiply the numbers outside the square root and keep the square root itself: (4√2 * 22) = 88√2

Step 3: Calculate (√11 + 3)² First, evaluate (√11 + 3): √11 remains unchanged. (√11 + 3)² = (√11 + 3) * (√11 + 3) Using the formula (a + b)² = a² + 2ab + b², we can expand the expression: (√11 + 3) * (√11 + 3) = √11 * √11 + 2 * √11 * 3 + 3 * 3 Simplifying further: (√11 + 3) * (√11 + 3) = 11 + 6√11 + 9 (√11 + 3)² = 20 + 6√11

Step 4: Calculate 6√113 This is already in its simplified form.

Step 5: Calculate (2 + √3)² Using the formula (a + b)² = a² + 2ab + b², we can expand the expression: (2 + √3)² = 2² + 2 * 2 * √3 + (√3)² Simplifying further: (2 + √3)² = 4 + 4√3 + 3 (2 + √3)² = 7 + 4√3

Step 6: Calculate (2 - √3)² Using the formula (a - b)² = a² - 2ab + b², we can expand the expression: (2 - √3)² = 2² - 2 * 2 * √3 + (√3)² Simplifying further: (2 - √3)² = 4 - 4√3 + 3 (2 - √3)² = 7 - 4√3

Step 7: Calculate (√21 * √14) To simplify this, we can multiply the numbers inside and outside the square roots: √21 * √14 = √(21 * 14) = √294 Breaking down 294 into its prime factors, we get: √294 = √(2 * 3 * 7²) = 7√6

Step 8: Calculate (√6 + 7√6) To simplify this, we can combine like terms: √6 + 7√6 = 8√6

Step 9: Calculate (88√2 + 20 + 6√11 - 6√113 + 7 + 4√3 + 7 - 4√3 + 8√6) Combining like terms: 88√2 + 20 + 6√11 - 6√113 + 7 + 4√3 + 7 - 4√3 + 8√6 = 88√2 + 20 + 6√11 - 6√113 + 7 + 7 + 8√6 Simplifying further: 88√2 + 20 + 6√11 - 6√113 + 7 + 7 + 8√6 = 88√2 + 6√11 - 6√113 + 14 + 8√6

Finally, the simplified expression is: 88√2 + 6√11 - 6√113 + 14 + 8√6