Question

1.Внести множитель под знак корня 1)4√3 2)-2√5 3)p√6,если p<0 4)-k√8,если k>0 2. сравнить значение выражения 1) 5√3 и 3√5 2)√7-1/√7+1 и 2√2/√2+1 3. Выполните действия 1)√28×√112 2)√559/√13 3)√162-√2/√2 4)(5+3√11)^2 5)(2√3+√108-√300)×√3 6)(2√7-6√3)(6√3+ 2 √7 ) 4.Сократите дробь 1)m^2-28/√28+m 2)(√5+m)^2/m^2-5 5.Вычислите значение выражения при t=-5,p=-1/2 1)25√t^6p^2 2)3√-p×4√-p^3t^2 6. Вычислите значение выражений 1)√(k+2)^2-8k + k,если k=-5491,7 7. Избавьтесь от иррациональности в знаменателе 1)3/√18 2)4/2+3√5 3)7/3√2-√7 8. Решите уравнение 1)-x^2+36=0 2)x^2=31 3)√14-x=13 4)√5+3x/5+3x=0 5)(√-x)^4=11 9.Решите неравенство 1)√x>12

Answer 1

1) 4√3 = √(16*3) = √48
2)-2√5  = -√(4*5) = -√20
3)p√6,если p<0 = √p^2*6
4)-k√8,если k>0 = -√k^2*8

2. сравнить значение выражения 
1) 5√3 > 3√5 т.к.
   √75  >  √45



3. Выполните действия
1)√28×√112 = √28*112 = √3136 = 56
2)√559/√13 = √43*13\√13 = √43
3)√162-√2/√2 = (√2*√81 - √2)\√2 = √2*(9-1)\√2 = 8
4)(5+3√11)^2 = 25+30√11+11 = 36+30√11
5)(2√3+√108-√300)×√3 = 2*(√3)^2 + √324 - √900 = 6+18-30 = -6
6)(2√7-6√3)(6√3+ 2 √7 ) = 28-108 = -80
4.Сократите дробь
1)m^2-28/√28+m = m-√28
2)(√5+m)^2/m^2-5 = 1\m-√5
5.Вычислите значение выражения при t=-5,p=-1/2
1)25√t^6p^2
2)3√-p×4√-p^3t^2
6. Вычислите значение выражений
1)√(k+2)^2-8k + k,если k=-5491,7
7. Избавьтесь от иррациональности в знаменателе 
1)3/√18
2)4/2+3√5
3)7/3√2-√7
8. Решите уравнение
1)-x^2+36=0
2)x^2=31
3)√14-x=13
4)√5+3x/5+3x=0
5)(√-x)^4=11
9.Решите неравенство 
1)√x>12

Answer 2

1. Внести множитель под знак корня

1) 4√3: To bring the multiplier under the square root, we can multiply the number outside the square root by the square root of the multiplier.

4√3 = √(4 * 3) = √12

2) -2√5: Similarly, to bring the multiplier under the square root, we can multiply the number outside the square root by the square root of the multiplier.

-2√5 = -√(2 * 5) = -√10

3) p√6, if p < 0: Since p < 0, we can bring the multiplier under the square root by multiplying the number outside the square root by the square root of the multiplier.

p√6 = -√(p^2 * 6) = -√(6p^2)

4) -k√8, if k > 0: Since k > 0, we can bring the multiplier under the square root by multiplying the number outside the square root by the square root of the multiplier.

-k√8 = -√(k^2 * 8) = -√(8k^2)

2. Сравнить значение выражения

1) 5√3 and 3√5: To compare these expressions, we can calculate their approximate decimal values.

5√3 ≈ 8.6603 3√5 ≈ 6.7082

Since 8.6603 > 6.7082, we can conclude that 5√3 is greater than 3√5.

2) √7 - 1/√7 + 1 and 2√2/√2 + 1: To compare these expressions, we can simplify them.

√7 - 1/√7 + 1 = √7 + 1/√7 2√2/√2 + 1 = 2 + 1

Since √7 + 1/√7 ≈ 4.4495 and 2 + 1 = 3, we can conclude that √7 - 1/√7 + 1 is greater than 2√2/√2 + 1.

3. Выполните действия

1) √28 × √112: To simplify this expression, we can multiply the numbers under the square roots.

√28 × √112 = √(28 × 112) = √3136 = 56

2) √559/√13: To simplify this expression, we can divide the numbers under the square roots.

√559/√13 = √(559/13) ≈ 7.1517

3) √162 - √2/√2: To simplify this expression, we can subtract the numbers under the square roots.

√162 - √2/√2 = √162 - 1 = 13 - 1 = 12

4) (5 + 3√11)^2: To simplify this expression, we can expand it using the square of a binomial formula.

(5 + 3√11)^2 = (5 + 3√11)(5 + 3√11) = 5^2 + 2(5)(3√11) + (3√11)^2 = 25 + 30√11 + 9(11) = 25 + 30√11 + 99 = 124 + 30√11

5) (2√3 + √108 - √300) × √3: To simplify this expression, we can distribute the square root to each term inside the parentheses.

(2√3 + √108 - √300) × √3 = 2√3 × √3 + √108 × √3 - √300 × √3 = 2√(3 × 3) + √(108 × 3) - √(300 × 3) = 2√9 + √(324) - √(900) = 2(3) + 18 - 30 = 6 + 18 - 30 = -6

4. Сократите дробь

1) (m^2 - 28)/(√28 + m + 2): To simplify this fraction, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.

(m^2 - 28)/(√28 + m + 2) * (√28 - m - 2)/(√28 - m - 2) = (m^2 - 28)(√28 - m - 2)/(28 - (m + 2)^2) = (m^2 - 28)(√28 - m - 2)/(28 - m^2 - 4m - 4) = (m^2 - 28)(√28 - m - 2)/(-m^2 - 4m + 24) = - (√28 - m - 2)(m^2 - 28)/(m^2 + 4m - 24) = - (√28 - m - 2)(m - 2)(m + 4)/(m + 6)(m - 4) = - (√28 - m - 2)(m + 4)/(m + 6)

2) (√5 + m)^2/(m^2 - 5): To simplify this fraction, we can expand the numerator and simplify.

(√5 + m)^2/(m^2 - 5) = (√5 + m)(√5 + m)/(m^2 - 5) = (5 + 2√5m + m^2)/(m^2 - 5)

5. Вычислите значение выражения при t = -5, p = -1/2

1) 25√t^6p^2: To calculate the value of this expression, we substitute t = -5 and p = -1/2.

25√t^6p^2 = 25√(-5)^6(-1/2)^2 = 25√15625/4 = 25√3906.25 ≈ 25 * 62.5 = 1562.5

2) 3√-p × 4√-p^3t^2: To calculate the value of this expression, we substitute t = -5 and p = -1/2.

3√-p × 4√-p^3t^2 = 3√(-(-1/2)) × 4√(-(-1/2)^3(-5)^2) = 3√(1/2) × 4√(1/2)^3 * 25 = 3√(1/2) × 4√(1/8) * 25 = 3 * (1/√2) * 4 * (1/√2) * 25 = 3 * 1 * 4 * 1 * 25 = 300

6. Вычислите значение выражений

1) √(k + 2)^2 - 8k + k, если k = -5491.7: To calculate the value of this expression, we substitute k = -5491.7.

√(k + 2)^2 - 8k + k = √(-5491.7 + 2)^2 - 8(-5491.7) + (-5491.7) = √(-5491.7 + 2)^2 + 8(5491.7) - 5491.7 = √(-5491.7)^2 + 43933.6 - 5491.7 = 5491.7 + 43933.6 - 5491.7 = 43933.6

7. Избавьтесь от иррациональности в знаменателе

1) 3/√18: To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √18.

3/√18 = 3/√(9 * 2) = 3/(√9 * √2) = 3/(3 * √2) = 1/√2 = √2/2

2) 4/2 + 3√5: This expression is already simplified.

4/2 + 3√5 = 2 + 3√5

3) 7/3√2 - √7: To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √2.

7/3√2 - √7 = 7√2/(3√2 * √2) - √7 = 7√2/(3 * 2) - √7 = 7√2/6 - √7

4) 3/√(2 - √7):