Solve (\sqrt{2}+\sqrt{3})^5

Question

Calculate the value

1092 + 893

Alternative Form

\approx 308.3018

Evaluate

(2 + 3)^{5}

Expand the expression

(50) (2)^{5} (3)^{0} + (51) (2)^{4} (3)^{1} + (52) (2)^{3} (3)^{2} + (53) (2)^{2} (3)^{3} + (54) (2)^{1} (3)^{4} + (55) (2)^{0} (3)^{5}

Expand the expression

More Steps

Evaluate

(50) (2)^{5} (3)^{0}

Evaluate the power

(50) (2)^{5} \times 1

Expand the expression

\frac{5 !}{0 ! \times ( 5 - 0 ) !} \times (2)^{5} \times 1

Removing 0 doesn't change the value,so remove it from the expression

\frac{5 !}{0 ! \times 5 !} \times (2)^{5} \times 1

Reduce the fraction

\frac{5 !}{5 !} \times (2)^{5} \times 1

Divide the terms

1 \times (2)^{5} \times 1

Multiply the terms

(2)^{5}

Use n a^{m} = n a^{m} to rewrite the expression

2^{5}

Rewrite the exponent as a sum where one of the addends is a multiple of the index

2^{4 + 1}

Use a^{m + n} = a^{m} \times a^{n} to expand the expression

2^{4} \times 2

The root of a product is equal to the product of the roots of each factor

2^{4} \times 2

Reduce the index of the radical and exponent with 2

2^{2} 2

2^{2} 2 + (51) (2)^{4} (3)^{1} + (52) (2)^{3} (3)^{2} + (53) (2)^{2} (3)^{3} + (54) (2)^{1} (3)^{4} + (55) (2)^{0} (3)^{5}

Expand the expression

More Steps

Evaluate

(51) (2)^{4} (3)^{1}

Expand the expression

\frac{5 !}{1 ! \times ( 5 - 1 ) !} \times (2)^{4} (3)^{1}

Subtract the numbers

\frac{5 !}{1 ! \times 4 !} \times (2)^{4} (3)^{1}

Reduce the fraction

\frac{5 !}{4 !} \times (2)^{4} (3)^{1}

Reduce the fraction

More Steps

Evaluate

\frac{5 !}{4 !}

Expand the expression

\frac{5 \times 4 !}{4 !}

Simplify

5

5 (2)^{4} (3)^{1}

Evaluate the power

5 (2)^{4} 3

Multiply the terms

More Steps

Evaluate

5 (2)^{4}

Evaluate the power

5 \times 4

Multiply the numbers

20

203

2^{2} 2 + 203 + (52) (2)^{3} (3)^{2} + (53) (2)^{2} (3)^{3} + (54) (2)^{1} (3)^{4} + (55) (2)^{0} (3)^{5}

Expand the expression

More Steps

Evaluate

(52) (2)^{3} (3)^{2}

Expand the expression

\frac{5 !}{2 ! \times ( 5 - 2 ) !} \times (2)^{3} (3)^{2}

Subtract the numbers

\frac{5 !}{2 ! \times 3 !} \times (2)^{3} (3)^{2}

Reduce the fraction

More Steps

Evaluate

\frac{5 !}{2 ! \times 3 !}

Expand the expression

\frac{5 \times 4 \times 3 \times 2 !}{2 ! \times 3 !}

Simplify

\frac{5 \times 4 \times 3}{3 !}

\frac{5 \times 4 \times 3}{3 !} \times (2)^{3} (3)^{2}

Multiply the terms

More Steps

Multiply the terms

5 \times 4 \times 3

Multiply the terms

20 \times 3

Multiply the numbers

60

\frac{60}{3 !} \times (2)^{3} (3)^{2}

Divide the terms

More Steps

Evaluate

\frac{60}{3 !}

Calculate the value

\frac{60}{6}

Reduce the fraction

10

10 (2)^{3} (3)^{2}

Multiply the terms

More Steps

Evaluate

10 (2)^{3}

Evaluate the power

10 \times 22

Multiply the numbers

202

202 \times (3)^{2}

Multiply the terms

More Steps

Evaluate

20 (3)^{2}

Evaluate the power

20 \times 3

Multiply the numbers

60

602

2^{2} 2 + 203 + 602 + (53) (2)^{2} (3)^{3} + (54) (2)^{1} (3)^{4} + (55) (2)^{0} (3)^{5}

Expand the expression

More Steps

Evaluate

(53) (2)^{2} (3)^{3}

Expand the expression

\frac{5 !}{3 ! \times ( 5 - 3 ) !} \times (2)^{2} (3)^{3}

Subtract the numbers

\frac{5 !}{3 ! \times 2 !} \times (2)^{2} (3)^{3}

Reduce the fraction

More Steps

Evaluate

\frac{5 !}{3 ! \times 2 !}

Expand the expression

\frac{5 \times 4 \times 3 !}{3 ! \times 2 !}

Simplify

\frac{5 \times 4}{2 !}

\frac{5 \times 4}{2 !} \times (2)^{2} (3)^{3}

Multiply the numbers

\frac{20}{2 !} \times (2)^{2} (3)^{3}

Divide the terms

More Steps

Evaluate

\frac{20}{2 !}

Calculate the value

\frac{20}{2}

Reduce the fraction

10

10 (2)^{2} (3)^{3}

Multiply the terms

More Steps

Evaluate

10 (2)^{2}

Evaluate the power

10 \times 2

Multiply the numbers

20

20 (3)^{3}

Evaluate the power

20 \times 33

Multiply the numbers

603

2^{2} 2 + 203 + 602 + 603 + (54) (2)^{1} (3)^{4} + (55) (2)^{0} (3)^{5}

Expand the expression

More Steps

Evaluate

(54) (2)^{1} (3)^{4}

Expand the expression

\frac{5 !}{4 ! \times ( 5 - 4 ) !} \times (2)^{1} (3)^{4}

Subtract the numbers

\frac{5 !}{4 ! \times 1 !} \times (2)^{1} (3)^{4}

Reduce the fraction

More Steps

Evaluate

\frac{5 !}{4 ! \times 1 !}

Expand the expression

\frac{5 \times 4 !}{4 ! \times 1 !}

Simplify

\frac{5}{1 !}

\frac{5}{1 !} \times (2)^{1} (3)^{4}

Calculate the value

5 (2)^{1} (3)^{4}

Evaluate the power

52 \times (3)^{4}

Multiply the terms

More Steps

Evaluate

5 (3)^{4}

Evaluate the power

5 \times 9

Multiply the numbers

45

452

2^{2} 2 + 203 + 602 + 603 + 452 + (55) (2)^{0} (3)^{5}

Expand the expression

More Steps

Evaluate

(55) (2)^{0} (3)^{5}

Evaluate the power

(55) \times 1 \times (3)^{5}

Expand the expression

\frac{5 !}{5 ! \times ( 5 - 5 ) !} \times 1 \times (3)^{5}

Subtract the terms

\frac{5 !}{5 ! \times 0 !} \times 1 \times (3)^{5}

Reduce the fraction

\frac{1}{0 !} \times 1 \times (3)^{5}

Calculate the value

1 \times 1 \times (3)^{5}

Multiply the terms

(3)^{5}

Use n a^{m} = n a^{m} to rewrite the expression

3^{5}

Rewrite the exponent as a sum where one of the addends is a multiple of the index

3^{4 + 1}

Use a^{m + n} = a^{m} \times a^{n} to expand the expression

3^{4} \times 3

The root of a product is equal to the product of the roots of each factor

3^{4} \times 3

Reduce the index of the radical and exponent with 2

3^{2} 3

2^{2} 2 + 203 + 602 + 603 + 452 + 3^{2} 3

Evaluate the power

42 + 203 + 602 + 603 + 452 + 3^{2} 3

Evaluate the power

42 + 203 + 602 + 603 + 452 + 93

Add the numbers

More Steps

Evaluate

42 + 602 + 452

Collect like terms by calculating the sum or difference of their coefficients

(4 + 60 + 45) 2

Add the numbers

1092

1092 + 203 + 603 + 93

Solution

More Steps

Evaluate

203 + 603 + 93

Collect like terms by calculating the sum or difference of their coefficients

(20 + 60 + 9) 3

Add the numbers

893

1092 + 893

Alternative Form

\approx 308.3018

Show Solution